I'm posting this in case it helps anyone else...

My engine suddenly started rumbling and running horribly rough. The Check Engine Light (CEL) came on . (It happened after I started the car with the gas gauge on "E" so so I was afraid that I damaged the fuel pump or clogged the filter, but no.)

My OBDII dongle showed a fault code of P0303- which is for misfires on cylinder 3. (P0301, P0302, P0303, & P0304 are misfires for cylinders #1, #2,#3, & #4, respectively, while P0300 is for random misfires, I believe.)

Over the years I've had similar symptoms on both of my 1996 2.4L Cavalier convertibles which I solved it by replacing the ignition-coil housing-- which is a pretty easy DIY job if you're somewhat handy. So I suspected the ignition-coil-housing went bad again, but no. Since I have two 2.4L Cavliers, I swapped the ignition-coil-housing and coils from the working Cavalier to the misfiring one, and it worked fine. So then I put the known-good coils into the questionable housing, and it worked fine. So then I knew that the housing was fine and that one of the coil-packs had failed. Based on the P0303 fault code, I knew it was the coil for cylinder 3, but I wasn't sure which cylinder was #3 or which coil-pack feeds cylinder #3. (One might expect that cylinder #3 would be the 3rd from the left as your facing the front of the car, but that seemed too easy for a GM vehicle. But I looked it up online and it turns out that it really is that intuitive.) I found a diagram online that showed which coil-pack feeds which cylinders. The coil-pack closest to the main electrical connector feeds cylinders #1 & #4, and the further coil-pack feeds cylinders #2 & #3. I replaced the coil-pack for #2 & #3, and that fixed it.

I happened to have a spare coil-pack, I think because I bought a pair of them on Amazon the last time that I had a coil-pack failure. I think a pair cost me less than one, or something. Glad I had a spare so that I could get my car running quickly (and cheaply).

Bottom line: If you have such an error, it may be your ignition coil housing. (Unfortunately there's no way to test it with an electrical tester because the failure stems from arcing-shorts that only occurs at very high voltage). Otherwise, there's a good chance that the problem is a failed coil-pack.