weak fuel pump.
check for a vehicle theft system?? Is the Light Illuminated. does it stay on:::
My car starts and runs fine .Yours may need a fuel filter or pump.
sounds like a fuel problem change the fuel filter first
check you ecu under the kick plat on the pasanger side then you might have to change you ptu
dd
The fuel filter is clogged or the carburetor needs to be cleaned and/or adjusted.
Check your maf sensor, the computer may not realize the engine is running because it is sensing no air flow, aside from that and a malfunctioning cam or crank sensor it could be a hundred things, what you need is a bit more information about HOW its not running before you can find a definitive why.
Its out of gas
get a new engine DUMMY!
To answer your question I need to know the year model of your Chevy Celebrity as well as the engine that it has in it.1996 chevy calavlier 2.2
lack of fuel
check ignition