That's a helpful clue about the non-original chargers. If the chargers you have don't have the same output capacity as the original charger, that could easily explain your problem. Frankly using any chargers that don't have exactly the same electrical specifications as the original is a rather dicey idea. It could damage the laptop, the charger, up to and including an electrical fire.
First thing you should do to start diagnosing this problem is find yourself an original charger for the unit. Either buy one from HP or check eBay for someone selling one or the same unit for parts because of a broken display or something like that. Contact the seller, see if they'd be willing to sell you the charger separately. Once you have an original charger, if the problem persists we can go from there.
I was recently given an old Compaq Presario X1000, I re-installed Windows XP onto it, and bought a new battery because the old one wouldn't charge.
Well this new battery will charge to 100%, then the battery stops charging and the charge gradually falls to 0% over the course of a few hours and the computer dies. Sometimes I can prevent this if I unplug the charger and plug it back in, then it starts charging back toward 100% again.
I should mention I do not have the original charger for this laptop, although I do have two different ones that it will run off of.