Why isn't the new starter on my 2004 Cavalier working properly?
It seems, more often than not, aftermarket starters just aren't built as well as factory. I've had the issue before that starters purchased from certain chains would not perform as well as other chains, and / or their starters were defective out of the box. Another problem could be that you may have forgotten to put the shims in place that the original starter had, which would cause issues too.
It could also be that your starter wasn't the problem - a wire was ( and is ) the problem. First, feel the length of the battery cables. If either cable is lumpy under the covering, than that wire is corroded inside and needs to be replaced. Then check the wires from the solenoid ( small cylinder attached to the starter) for lumpiness. You didn't mention what the problem is, so I'm trying to cover all the bases here. knowing the exact problem would help me help you.
If everything checks out ok, then you'll need to pull the starter out and have it bench tested for resistance, to see if it or the solenoid is defective. I don't want to slam any particular chain store here, so I won't say who I've had trouble with.
Anyways, check these things out and, if everything checks out good but it still drags or barely starts, then you may have a problem with the ground strap, which is a flat, somewhat wide braided bare wire that connects the engine block to the chassis or body of the car. While checking wires, inspect the connectors for green or white deposits - these will stop the starter from working too!!