My question involves landlord-tenant law in the State of: Texas

The brand new apartment building I started living in from 07/2014 switched management at the beginning of 2015, but I loved my apartment so much at that time that I was absolutely sure I wanted to renew my lease for when my current lease expired. Turns out, the new management company does not maintain the facilities very well, lets dog feces pile up, lets both elevators go out for weeks at a time, and among other things let us go 6-7 days without working AC in the 100+ degree Texas heat. We got a window unit, but that only got us to about 85-90 degrees.

Anyway, my old lease is set to expire and the new lease will take effect in mid October and I have already signed most of the lease. When I say that I have signed most of the lease, I mistakenly forgot to sign some addenda and some pages of the lease document when I originally filled it out. I have already given 60 days notice to the management and want to know whether these incomplete/unsigned parts of the lease make the document as a whole incomplete. They have told us that because they have already renewed us in their system, that our giving 60 days notice will cause us to break our new lease contract.

Do I have any grounds to not be subject to an early termination penalty based on the fact that the document is not yet complete?