95 cavalier barely starts/ shuts off after moving

Hello I'm new to this forum, and have had countless problems with my 95 Cavalier I bought a year ago. Was driving it to work this morning and heard a loud pop, and then the car wouldn't start. When it finally did start up, it would stay running until I either put it in 'drive' and accelerated, or even just let the car coast on its own, and it would shut off. I can't think of any problem it may be.
Anyone who may know something please let me know.
Thanks

It sounds like it could be the fuel pump. In my dads '95 Cavalier if you have nothing on (radio, heater, etc.) you should hear it come on for a brief 2 seconds when you first turn on the key. If you don't hear it, check all the fuel pump fuses and if they are good, it is probably your fuel pump. How many miles are on it?