Q:

How can a GM prevent growing disillusioned with their own game?

I recently began a new game in which I gave the players much more free reign in designing their characters than I might have in the past.  What I wound up with was a very morally-diverse party, with each of the characters having extremely different goals and intended means of achieving them.  (I'll edit in more game-specific details later, if people want them; I'm attempting to keep the original description and question brief.)
What this means is that it is a mostly selfish, evil-slanted group, each member of which is out pretty much entirely for himself.  I really dislike railroading in games, so I attempt to have a more "open world" feel, however I had to railroad the first session very hard in order to make the party to even be a party.  This made me very unhappy as a GM, and I could tell that it made at least one of the players unhappy as well.
Fortunately, I shouldn't have to railroad them like that again now that I've forced them into a situation where they have no real choice but to rely on each other to survive.  (They're stranded in an unknown jungle with only each other for support; wandering off alone would literally be suicide.)  But I've discovered in the course of that first session just how much I dislike their party, and I realized something: I don't think I'm interested in telling or participating in a story about evil people doing evil things.  I love all of their character concepts individually, but as a whole it simply doesn't make a compelling story.
Maybe I'm simply expecting too much character development from the first session, and maybe I'm not giving them enough time to really come together, be more complicated, and prove to me that their motivations are more intriguing and complex than "screw the world, let it burn".  But I'm suffering from severe disillusionment for the game, to the point where I'm honestly not even interested in running it anymore.
Is there any way I can reverse this or somehow patch the situation to make it better for me?  I want to keep running the game for them, but I don't know if I can do it if I hate every minute of it.

A:

One of the things I say first when I'm about to start running a game for a new group of players is that it is not my responsibility to come up with increasingly convoluted reasons why a disparate set of characters with nothing in common should adventure together. I've been there and tried it, and it is stressful, frustrating and simply not fun. I'd much rather spend my time coming up with cool stories and fun situations that everyone can enjoy.
Given you've got a set of characters and you'd rather not have to get the players to start all over again, what I suggest you do is put the responsibility on the players to come up with reasons why those characters should be working together. This may or may not require them to make changes to their characters' backgrounds and/or motivations, but if you want a situation where you have a workable party of PCs that you have some chance of enjoying GMing for, I really don't see that you have much other choice.
I advise that you do this as a group rather than individually so that players can bounce ideas off of each other. That way you are more likely to end up with creative and entertaining interconnections that are fun to work with and use as plot hooks.

A:

I ran into this too, with the diverse characters and the hard first-session railroad. I became disillusioned because they wanted me to tell a story and I wanted a sandbox, but the result was the same: I had no desire left to run it.
It's awful advice, but my conclusion was that not every game is made to be continued, and it's only a failure if it's pushed beyond the number of sessions it can happily support.
You might be able to completely turn it around, but it's a tall order to change the game into something more like what you'd be happy with when it's contrary to what the players are already enjoying about the game. If you can pull it off, do it. You might consider offering to give up the GMing of this game to another player, and become a player yourself.
But if you can't pull it off, letting the game die peacefully is kinder to you and the other players. The sooner a doomed game is done, the sooner you can start on the next awesome one!

A:

Talk to the players
Others have said it, but this can't be over emphasized.  Most traditional RPGs are collaborative affairs and the GM cannot be responsible for making everyone happy.  So talk to them plainly and see what they want.  They may be highly supportive of ending this campaign and starting a new one or of working with you to change the direction of the game or any number of other options that you can all partake in as a team.
Railroading is not an either/or
You mention that you hate railroading, which I totally understand.  But realize that most campaigns will not be and should not be "railroading or open world".  It is much more of a spectrum of "some railroading and some open world, but with varying amounts".  And the amount can vary not just between games but within one campaign.  It may be helpful to railroad fairly heavily at the beginning of a campaign as you get the world established, get the characters fully established and grounded, and get some of the potential plots established.  Then you can ease up and move more open world when all of the characters have motivations well established and plot hooks sunk deep.
Evil can mean a lot of things
You said that most of the characters ended up evil, but that can  mean a lot of things.  An evil character that just wants to make the world burn (probably) isn't well developed or interesting as anything but an excuse for Hero to get into fights.  
However, an evil character with a backstory for why they are evil and a specific motivation can be very interesting, sympathetic, and even hold onto a code of honor while definitely being evil.  Shylock is (often, there are multiple interpetations) portrayed as evil and greedy, but also in a sympathetic and relatable way and gets one of the most eloquent speeches Shakespeare ever wrote.  Strahd in Vampire of Mists is unflinchingly evil, but his fall to evil was relatable and sympathetic and even when it was complete he held to code of honor similar to chivalry.
In short, it is possible that your loathing for these evil characters will fade somewhat if you work with the players to make sure they have well developed evil characters that have a strong motivation and some (preferably sympathetic) explanation for why they are evil.
Also, if evil to them just means "greedy" but not in a "watch the world burn" sort of way...well that isn't all that different from the way most good characters act in many rpgs.  It just means that you need to shift plot hooks from things like "Help us, the orcs are attacking" to "Help us, the orcs are attacking and we can reward our rescuers handsomely".
Edit: an example
I closed this out, but then thought an example might help.  A character whose motivation is "I want to plunder and kill" is evil, but boring.  I wouldn't enjoy gming for that.  
But lets say we have a character that starts out with "As a child of 6 I watched the Medici's stab my father, the rightful king of Alonion, dishonor my mother, and throw my older brother out of a window.  They destroyed my family and stole my throne.  I survived only because my nursemaid grabbed me and ran and then gave me to farmers to raise."  Now we have something of a background and plot hooks.  But its not necessarily evil, many good characters in fantasy have a somewhat similar background story.
So we add, "The Medici's that did this are now dead or old and retired.  It is their son, who is my own age and didn't participate in the slaughter, that now sits on my throne.  He leads the people well and does his best to rule fairly.  Yet the throne is mine by rights and I will still seek to regain it."  Now we are probably into evil territory, and we can talk about how evil and lawful v. chaotic based on how he intends to go about it and what he is willing to do or not do.  But even if we go deep into evil, there is a reason for it and it is interesting with a very sympathetic justification.
But now we need to explain why he is off adventuring instead of trying to raise rebels (unless you want the game to be about him trying to raise rebels right off the bat.)  So we add, "I know that I have little hope of regaining my throne without vast sums of money, personal experience, and a reputation for power and leadership.  Thus, I set off now to make a name and a fortune.  My sights remain firmly on my kingdom and I will do whatever it takes to gain the money I need to finance my war, but for now I work elsewhere and prepare..."
Now, we have a sympathetic reason he is evil, have established that he is willing to use at least some evil means to achieve his ends which are arguably evil, have plot hooks that could be used later, but also have a reason he is running around with first level adventurers doing more or less standard first level things.  
Personally, I would be happy to gm for that character. If my players wanted to play evil characters I might try to help guide them to a story like that and the motivations that come with it.

