I usually can. Can you give me a more in depth description of the symptoms and what happened right before it quit POSTing?
Since it's HP, I've got my money on the video chip as well. They are notorious for coming desoldered. The usual fix is to insert a shim between the case and the chip, which applies pressure and keeps the connections. A more permanent way to fix it would be to use a heat gun with a very fine tip to melt and reflow the solder. You could also use an oven, but I don't recommend this because of the extreme complexity of the motherboard, which makes it much more likely for something else to get messed up.