I have a 1992 Lumina Z34 with a 5-speed. I was taking off from a hill when both axles busted. The left one broke the inner CV joint; the right one broke the outer one. Does anyone have any idea of what may have happened? I'm also having a problem with the rear brake lights staying on.

take off a little slower and do not ride the brakes or it could be just a fluke that they broke. and as for your brake lights I hate those kind of problems

They were just ready to go I guess...
As for the brake lights, you may want to check the turn signal switch and the brake switch that is mounted down near the pedal.