How binding is a non-compete for a contracting consultant?

I coordinated the billing for a consulting assignment at Company X through a contracting company. The contracting company required that I sign a non-compete agreement ensuring that I do not work for Company X unless I bill through them. At the end of the assignment, the contracting company was unaware of any other assignments and terminated by employment reminding me of my non-compete agreement. Simply stated, they have no work for me. Another contracting company is aware of several assignments at Company X. I have no work and being a contractor do not collect unemployment. It feels reasonable to me that I should be able to go through another contracting company to gain some employment. What do you recommend?