how to get out of a non compete

I am currently a account manager for a contracted cleaning company and I work out of a nursing home. The company is going to pull out from the building because they are not getting paid. However the adminstrator of the building wants me to come work for her as in house housekeeping, but I signed a non compete for my company a month back. When I signed the form they faxed it over to me, and then I faxed it back. There is a spot for someone else to sign it, but they didn't actually sign it with me. The company also runs another building, and my adminstrator thought if I was on the payroll for the other building and worked for both but ran this one if that was a way around the form. I guess what I am trying to figure out is if there is any way to get out a non compete or what could happen if I quit my company and work for her.