1988 Chevy Camaro

I also have a 1988 Camaro, V-Sux though, and I was going through similar problems. There are several things to check. 1) Is the engine getting fuel? 2) Is your timing correct? 3) Have you checked the spark plugs and spark plug wires?
Let me go into detail. With Item 1, you should check your fuel pump (make sure it is the correct one for either carburated or fuel-injected) for functionality. Next, your fuel filter. A clogged fuel filter may inhibit the flow of fuel from the tank either partially or completely. My engine is Multi-Port Fuel-Injected (MPFI), so I also checked my fuel injectors. I'm not sure about carburated models what the equivilant would be. To sum Item 1 up, make sure that there is nothing inhibiting the flow of fuel to your engine.
Item 2: Timing. If your timing is off, the car may not start. Since you replaced the distributor, it is a good idea to have your timing checked. Along with the distributor, have you replaced the rotor and cap? If at least one of these three components are faulty, it with throw off your ignition.
Spark Plugs and Wires. If you change your distributor, change your spark plugs and wires if they have not been changed RECENTLY (strong emphasis on that). Think of it as a three tier system. Spark plugs are 1, wires are 2, and distributor is 3. If you change 1, it is not necessary to change 2 or 3. If you change 3, then change 2 and 1. The higher the item on the tier you replace, you need to replace the items below it.
Since your car is turning over, your starter should be fine. Also, check your battery. Depending on how many times you have tried to start the car, your battery may be drained. Have it checked and charged. I had the same exact problem with my V-Sux and I did all of the above. The car fired up and ran, no problems. For me, it was a combination of everything: engine not getting fuel, a FRIED distributor, ate-up spark plugs and wires, and timing. Of course, make sure that components are installed properly. If you don't have a Haynes manual, I'd suggest getting one. They're relatively cheap, around $20, and are AWESOME. It's helped me a lot with my car.