Signed lease on 5/18/2012 before seeing apt. Upon entering with leasing consultant to do walk through immediately seen roaches, mold in freezer, major crack in ceiling,heavily stained and burnt carpet. I have giving them a chance to make repairs. So far they have sprayed for the roaches, and they went in the bedroom closet and cut a patch of carpet out and replace it with the burnt carpet area so now the burnt carpet is in the closet. They don't have anymore of units of my floor plan to move me to. They want to give me a bigger unit with rent I can't afford nor would qualify for. Can I break the lease St this point? Is the lease binding since my roommate haven't sign?

If the lease specified both of you as roommates, without your roommates signature you might be able to void the lease. But if you paid your security deposit then I believe you are bound. Since they are doing the repairs, you may not have an out.

Next time look before signing.

... Can I break the lease St this point? ...

No. Perhaps you could have if you sought to back out immediately upon seeing the premises. But your failure to do so immediately, and decision to move in, removes that option.l

I haven't move in yet and I did let my leasing consultant know immediately that the unit was unacceptable to me.