It sounds like you weren't laid off, you were contracting and your contract was terminated. Those are very different things.
Also, it sounds like you were bring paid in cash without any withholding, SS, Fica, etc. so it's true that you weren't paying into the unemployment fund and it will be hard to get anything out.
There is some possibility that you could claim that you were actually a full time employee rather than a contractor. The IRS loves this because then they get to penalize the employer and force them to back your unemployment and everything else. Of course, the employer isn't going to just hand over that money without any complaining, and you are also going to be found liable for failing to report your status correctly. Even if you could retroactively change your employment status, it's going to be hard to do, it's a sloppy deal and doesn't guarantee any positive results for you (many complexities).
I would start looking for more work, and be careful to ensure that you absolutely understand your payment/work status before you start!
FYI this is one of the many reasons that experienced contractors are very particular about forming entities, paying SE taxes, or otherwise making sure that your status is clear!