I too have a 96 Cavalier. I guarantee you the tapping noise is the timing chain. Every Cavalier I've seen has this problem because it's a big metal chain riding on a plastic tensioner. The tensioners always break causing a kink in the chain, then it breaks. I just recently had this problem with my car. If there's ever a tapping or slapping noise coming from under the hood it's the timing chain slapping because of the tensioner.
Maybe it's the way you're driving your Cavalier... or you just bought a crappy one. Because my 1996 Chevy Cavalier 5 speed runs like a champ.
1996 Chevy Cavalier ETS light. Electronic Theft System is what it stands for. Is your Check Engine Light on also? Usually the only time I see the ETS Light is when the Check Engine Light on too. I have never encountered just the ETS light on by itself.
I bought a 96 Cavalier off of Craigslist from some woman, and it was in such bad condition. But I needed a car bad, so I talked her down to $900 for it, and not even 5 minutes later the brake lines broke. I tried to call her and get my money back, but I could never get a hold of her or even find her again!
I had it towed to a Midas garage, and they found so many problems with it, it would have cost near $3000 if they fixed it all. I nit picked through what could wait and got it down to just $1000 in repairs there. They replaced the rear brake drums and cylinders, 3 pieces of brake line, had to get 4 new tires, and they threw in a free oil change because of it all. They did the brakes wrong and they go almost to the floor, but it stops. Midas refused to redo the job even though they messed it up. So now I am driving it daily AND still making new repairs when I can.
I replaced the serpentine belt, and had to put in a radio because the old one was ripped out. It needs new speakers because only one works right now, a new valve gasket because it slowly leaks oil, but it's hardly noticeable; I haven't put more than 1 quart of oil in since it last leaked 4 months ago.
Replaced the spark plugs because it had the wrong kind in it (they were FORD plugs!!).
Just replaced the front calipers, and now it turns out it's the master brake cylinder that needs replaced to get my brakes fully working, so I got that now too, as well as new front rotors ready to be put on.
Also I am having to replace all the wheel studs, because they keep breaking or stripping because of rust.
This car has been a huge headache, but it has allowed me to drive almost daily 100 miles to WV and back to see my girlfriend, and for school and home, despite its issues. So I love my car; I just can't wait until all the repairs and tuneups are done!