Q:

Can a Rogue, with Rogue Crawl, charge while prone?

Can a Rogue with Rogue Crawl (Ex), charge while prone and crawling.  Assume that there is just clear space and open ground between the rogue and the target.  I think it comes down to the line in charge, 'nothing can hinder your movement'.  Rogue Crawl lets you move at half speed while prone, so I'm not sure if your movement is officially hindered.  
I can't find a definition anywhere for 'hindered' movement, but I found one for 'hampered'.  They seem to be used interchangeably, as seen in Soften Earth and Stone, which uses hinder where they could have used hamper.
Looking at movement, they use the word hampered.  So our movement, while prone, is officially not hampered, as that would be the result of intervening difficult terrain, obstacles or poor visibility, of which there is none.
If the Rogue is hindered by being prone, would Freedom of Movement allow them to charge while prone, if they had the above feat?
Note: I realize that hamper's definition is 'to hinder', but I'm looking for a RAW explanation of if I can or can not do this.

A:

For lack of clearer rules I would have to say Yes, you are able to charge in this situation.
Why this would be the case comes down to a question I asked before, are you able to charge using alternative movement methods and the answer I got was as long as you had the correct movement speed, and fulfilled the other conditions of charge (straight line and all that). In this case the rogue talent gives you a special movement speed which is equal to half your base land speed.
This could be ruled just as easily in the opposite direction as its not directly called out as a crawl speed or new type of movement. So it's best to talk with whoever is running the game, and if it's you running the game, then be evil, lol.
I also have a real world example. I do rapier fencing and at a tournament I saw someone perform a Balestra (A footwork preparation, consisting of a jump forwards. It is most often, but not always, immediately followed by a lunge.) while on their knees. 
Also, do not forget that you will still take the -4 penalty on the attack because you are still prone.

A:

Technically, yes
Let us assume that all conditions for charging are met if the Rogue would stand. Now let us look at the requirements:

Movement During a Charge
You must move before your attack, not after

M'kay, will do!

You must move at least 10 feet (2 squares)...

Well, a crawling Rogue would be able to move at half speed. As soon as your speed is at least 20 feet, you would be able to do it.

...and may move up to double your speed directly toward the designated opponent.

Whoa! So, actually you would be moving at your normal speed.

You must have a clear path toward the opponent, and nothing can hinder your movement (such as difficult terrain or obstacles)

Well, it is a vague wording, but being prone doesn't seem to be something like difficult terrain or obstacles.

You must move to the closest space from which you can attack the opponent. If this space is occupied or otherwise blocked, you can’t charge. If any line from your starting space to the ending space passes through a square that blocks movement, slows movement, or contains a creature (even an ally), you can’t charge. Helpless creatures don’t stop a charge.
If you don’t have line of sight to the opponent at the start of your turn, you can’t charge that opponent.

We assume that it was already possible, the conditions are met. Notice that squares don't hinder your movement.
Prone condition description also doesn't disallow such a movement.
...but would you try in my group, I would just rule "No, you can't!", for obvious reasons. :)

