If my car jump time would it still try to turn over but slow?

SOURCE: car shuts off while driving.

Could be a fuel problem , but try this first. When coming to a stop or light, either put transmission in neutral or with two feet brake & hold the gas alittle. The reason for this is maybe your idle speed is too low , very common problem on these engines with 75k plus miles. The idle air passages can get clogged up with carbon & lower the idle speed. Could also be a sticking egr valve causing a vacuum leak that will let the engine run fine , but stall at idle speed.

SOURCE: WON'T START

There were problems with the ignition cylinder. Occasionally gets stuck and electrical contacts may not work properly.

SOURCE: no power, jerking bad 1998 cavalier

change your TPS (throttle postion switch)

SOURCE: My 2003 cavalier turns over but won't start, what is causing this

I would check if you have fuel getting to the motor.
When you turn key to the on position without engine turning over you should hear your fuel pump supplying gas to motor.

SOURCE: Batterty dead. Check engine light/Antifreeze pouring

The main problem could be a well known cobalt ignition issue. check all fuses, wires, and connections if you've worked on cars before and call to see if you still have any warranty left. This should be handled by a chevy dealer or chevy trained mechanic...to isolate the issue fast and avoid repeat visits to get er done.