If you do open the case, there should be some numbers on the power supply such as 12 volt Amps or just A
If you can take a picture of the label, it is even better.
The fastest thing HP offered from the factor was a 2400XT and the most power hungry card they ever added to that system took about 30 watts
A 5570 or GT 430 are about as good as i would guess from HPs own card selection. They both take a bit more power then HPs top card, but should still be within range of that power supply.
A 6670 would take about 2x HPs fastest cards power(about 60 watts but more like 45-50 in most games)
That said, these are both very low/entry level cards.
Remember, you need a low profile card for your system.