I purchased a V4000 in March, 2006. After a couple months, I had problems with the charger light staying on. I had to turn the plug to a certain position to get it to work. I didn't use the computer mutch so I put up with it. In October, my son took the computer to school and the problem started getting worse until the computer wouldn't boot up at all. We sent the computer in to HP and they said there was "liquid damage" to the computer and it would cost $739 to fix it. I only paid $799 for the computer new. We have never spilled any liquid on the computer.
And you can probably buy a better computer new for less. Sounds like you suffer from a bad dc-in connector on the motherboard. Center pin comes loose from the board, sometimes making contact, sometimes not. Take it apart yourself and resolder it, or put in another connector. Workaround is a all-in-one media cable or a docking station, they connect to the docking port, and power the computer through there. You know yourself if liquid was spilled, and errors started after that?