Will not hold a charge or turn on without being plugged in?

My girlfriend had a HP laptop with the same issues. What I determined happend was she had a bad habbit of walking around with it, while it was plugged in and not supporting the plug. The power supply plug, eventually broke a wire, so it would power the computer, but becuase the battery never received a charge it died. Replaced teh battery, same issue until i discoverd the issue was the power supply. I rebuilt it. Now in your case you've replaced both, leading me to beleive same scenario has occured, only the problem is with the jack in the side of your computer. probably got jared hard enough at one point that may have broke a solder joint.

One other thing you might consider is replacing the cmos battery (looks like a watch battery)