Getting letters of recommendation for a master's degree if I don't get along with my current advisor I'm currently in my final undergraduate year and I really want to go to graduate school, but there are some problems: I'm not sure if I can get recommendation letters. 

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My current advisor is insane and unfair. She didn't let me take part in a conference paper that she and another student worked on. That was a very good chance for me to improve my chances of getting to graduate school, but now it's lost. She slightly modified the Caesar cipher and the other student just wrote a program that demonstrates her "algorithm", and it took him several days, while I could've done that in 4-8 hours.

Second time around, I decided(took her advice) to take the research category in a course where we have to make a project my the end of the semester. She didn't guide me or provide me with any references or resources that could help me. She just tells me "write it and I'll read it" or "look it up and understand it". I spent most the semester trying to get my head around the research topic and implement the algorithms, until I finally had to change to the development category because I was going to fail the course otherwise. Now she tells me that "she lost trust in me" and that she won't waste her time with me again.
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So obviously my relationship with her is not very good, but what can I do now? Is doing research(or "research" in this case) at the undergraduate level mandatory for applying to graduate programs? My previous advisor liked me and my relationship with him was very good, but he left. If I could find him, can I get a recommendation letter from him? There is also another professor that is no longer at my school, can I get a recommendation letter from him as well? I've never worked on something with them or been their assistant, though.
A few points regarding your questions:


Presenting a weak conference paper is only very slightly better than presenting no paper at all. It may even be worse, if someone evaluating your application saw the presentation and came away unimpressed.
There is no requirement that you get a letter from someone like your present advisor. Such a relationship is clearly not productive for either of you, and including a letter would definitely not help.
You do need to get letters from people who can comment on your work skills, so your old advisor would be acceptable. Other people with whom you have worked—so long as it's technical in origin, even if it's not explicitly research—could also write letters for you. If you can't get three such letters, then you should get them from people who know you beyond taking classes with them. Only if you exhaust all other possibilities should you rely on people who know you only from classwork.
Finally, find yourself a new advisor, if at all possible.