I just installed the Geforce gtx 650TI... into my convertible minitower, just like yours, and I had to rip apart the back of the computer both to install the power supply and the card. Not recommended. The card is double-wide, which means it takes up two slots on the back of your computer, one of which bumps up against the case fan... basically the 16X pci whatever it is slot is too far up towards the power supply to accommodate one of these cards. And also the casing around where the power supply goes is proprietary and blocks the power cord of standard power supplies. Thanks HP. Thanks a lot.
Also my games are all fading to black, so maybe it's not even compatible for some other reason... but don't forget to research physical compatibility of both your video card and new power supply!