1989 Chevy Camaro behaves strangely when I slam on brakes

My Camaro has a few problems, and I'm sure they're connected. First of all, the Service Engine Soon light never goes off. Every once in a while when I have to almost slam on my brakes behind someone, my car starts acting funny and always displays the same symptoms--but usually goes away in a few hours or days. After that whenever I apply the brakes, it pulls to the left and is very hard to keep straight. Accelerating is also difficult because when I try to accelerate, the engine won't carry the car as far as it does when not experiencing these problems. It's also hard to press in the brakes when it's like this. I've also noticed that when on a downward slant in neutral and without the parking brake on, the car won't roll forward. When it's having these problems I can also smell rubber burning from under the hood, but I can't detect from where--although I'm sure it's the serpentine belt rubbing on something. If it makes any difference, my Camaro never had an A/C. It is also a 2.6L. Now when I apply the brake the car doesn't slow down until the pedal is to the floor. Can anybody help?