I couldn't find pictures of your system's internals. All I could find is this - you tell me if it looks like your computer, at least:
http://www6.pcmag.com/media/images/253769-hp-pavilion-p6741c-b-back.jpg
http://www.pcmag.com/slideshow_viewer/0,3253,l=262727&a=262436&po=5,00.asp
From the second link the 5th picture out of all 12 is especially interesting.
If that's your system, you should be able to fit the GPU you're interested in, but I've jsut spotted in the first picture that the side panel (left one as you're looking from the back of the tower) has a thumbscrew, which should greatly facilitate opening the case. If that's the case, please remove that thumbscrew and slide the panel back - take a picture of your computer's internals - I'd like to see your PSU, your motherboard and the slot configuration.
If this happens to be your motherboard, it's compatible:
http://support.hp.com/us-en/product/HP-Pavilion-p6000-Desktop-PC-series/5035348/model/5090667/document/c02560084/
According to this document, your power supply unit is capable of providing 250W and features no PCIExpress connectors. TheASUS GTX 750 1GB OC Edition doesn't require PCI Express connectors as it only needs the 75W provided through the motherboard slot. The Athlon II X4 640 your system seems to be equipped with (correct me if I'm wrong) can consume 170W, which is too close to the supposed 250W limit your PSU could have.
Get us a picture of your PC internals!
Based solely on the fact that the ASUS GPU doesn't require additional power straight from the power supply, I'd say you could use it in your PC, but I'm a little concerned about the power supply. If that one can't handle the ASUS GPU, you will experience bluescreens of death, sudden reboots and possibly end up with a computer that doesn't turn on anymore until you get a better power supply unit.