The first thing to do is to have a shop pull the computer codes or get a scanner from a place like AutoZone. That will help you pinpoint the problem and make this whole answer pointless. Does it crank/turn over? If not then you have a bad starting system. The starter motor is the most likely culprit, althought it could be a bad relay. If it does crank, then read on. Cars need three things to run: 1.Fuel 2. Air 3. Spark (Combustion). If the engine doesn't have all three in a reasonably ideal mix, then your engine will not run. If you'd like a more detailed explanation, e-mail me at fast_farmboy@Yahoo.com.
Or you could give about twenty attempts while holding the brake down when you start it like a stick shift. Then always start it while holding in the brake. The only way to make it so you don't have to hold the brake everytime you start it is to take it to someone who knows how to switch over the grey rally switch located under the hood....right in the front.
what are the signs for replacing the oil gasket in a 1996 Chevy cavalier
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Instructions on how to change the rear hub wheel bearings on a 1996 Chevy cavalier
do you mean cavalier hand brake?
Replace the fuel filter, that is a good place to start.
check this site out
Check the fuse!
it is under the dash at the top of the clutch pedal.it is the same as the clutch start switch
Providing your cavalier has a 2.2l, this is what your looking at.
in the fuel tank