Want to kill this car

I bought a 2003 Honda Accord with 90k 4 months ago. The headlights started dimming when you take your foot off the gas. I took it to the garage, they said the alternator was bad. Replaced it. Then a few days later, the system charging light stayed on, and I had to have the car towed. The garage said we tested your battery, that was bad too. They also said the check engine light was on, and it was giving a PCN (bad computer code).I took it to Honda, they said there is nothing wrong with the car, it was the “Non-honda alternator.” the headlights continued to dim. the other day I was driving, the ABS, BRAKE, seatbelt lights all came on and stayed on, the heater, radio and speedometer, power locks all shut off. I parked the car and it shut itself off a few minutes later. would not restart. had the car towed AGAIN, to a different garage, he couldn’t duplicate the problem, couldn’t find anything wrong with it. WHAT DO I DO with this stupid car?? I want to sell it, but I know that’s prob unethical if I don’t disclose everything, but who the heck would buy it otherwise???

Your should have at least a three month, 4000 mile warranty on the alternator. Have the shop check the output and verify whether it is in specs or not. If the alternator is bad, then it should be replaced free. Not very sympathetic with the Honda dealer excuse on alternator without providing enough information to you to go back to the first garage to get an alternator that meets specs. “Buy Honda OEM parts” is a non-starter for me. That said, it could be the rebuild alternator that you got is marginal or not within output specs. There may be other issues, but I would start there.

What about check engine light? Is it still on, or did a reset eliminate that issue?

This sounds like a power supply problem and while it’s impossible to diagnose over the net, you should consider a careful inspection of all main fuses (links) or the possibility of a failing ignition switch.

Many Hondas are under a Recall for switch problems which means if your car is in the year and VIN range you could get this repaired by Honda for free. You will have to call the dealer on this.
I’ll add that many Hondas may have switch problems of the same nature and they are not covered under a Recall. There’s a lot of backroom politics behind issues like this.

Dying and not starting could be related to the main relay; another problem area. It’s possible there could be more than one problem although dying and failing to restart could also be caused by the ign. switch.

Make sure the alternator is checked for “A/C ripple” which is produced by a weak or bad diode. THAT can cause all your symptoms…

If your headlights dim noticeably when the engine is idling, THAT is a sign of a weak battery…

the check engine light was reset by changing the battery; it has never come back on.

DID you change the battery? If the battery has several years on it, it would be a good idea to replace it.
If the battery is near new, disconnect the battery cables, inspect the cable terminals, clean the cable terminals and battery terminals with a wire brush, smear the terminals with Vaseline, and reconnect the cables.