You should check several things, starting with spark plugs and wires if it has them,fuel pressure/fuel filter,air filter,Tranny fluid level(automat.) clutch slipping(standard trans) brakes may not be released completely, and then on to more involved things like,worn camshaft,burned valves,timing issues,low compression,restricted exhaust. I worked on a Ford topaz once, and come to find out after MANY come-backs, It was the plastic bowl inside the gas tank heating up by the return fuel and causing it to distort the bottom of the bowl,it raising up, choking off the fuel pump's supply of gas.
with me it was the o2 censer
Low fuel pressure
In my experience with my Chevy it was a ground wire
have you checked your fuses?
Numerous things can cause a car to hesitate when trying to start. Almost always it has to do with the fuel delivery system. A dirty fuel filter, dirty injectors, worn fuel pump, fuel pressure regulator, etc. Most often the problem has to do with what kind of hesitation. With a 1998 Cavalier, I would start with the Injectors. STP???
Bad heater core.
The 2005 Cavalier could have a fuel leak. Have the entire fuel system checked, as a fuel leak can cause a dangerous fire.
There are several things that can cause your 1995 Chevy Cavalier transmission not to go into drive or reverse. The most common cause is a lack of transmission fluid. A broken shifting fork will also cause the problem.
Dead battery
bad o-rings or not seated and tightened down properly
Blown Head Gasket or Bad Cylinder Head
The 1997 Cavalier has two motor mounts, as well as a transmission mount. If the mounts are broken the motor can move around and cause damage to components under the hood.