First of all, I'm not sure what those two opamps on the input are for, all they do is supply +/10 to your transistor buffer. As far as I can see, and maybe I'm missing something, is the output(emitters) of the transistors drives the input to an integrator(U3A). The voltage into this integrator is dependent on the state of U4A. It has NOTHING to do with that 10V from the first stage, although I believe that's what you THINK should happen.
Regardless, your NPN transistor is, in fact, forward biased, as you can see by the Vbe=.67V. Your problem is that you've got too much (WAAAAAY too much) feedback around your comparator. Try changing R6 from 1K to maybe 50K.