I wouldn't say yes so quickly. Of course any 775 chip will physically fit on the board, it doesn't guarantee that your chipset or BIOS will support it. According to the link you showed above it only supports:
Processor upgrade information
Socket type: 775
Motherboard supports the following processor upgrades:
Intel Core 2 Duo (Wolfdale) E8xxx
Core 2 Duo E6xxx (Conroe) up to E6850
Core 2 Duo E4xxx (Conroe) up to E4400
Pentium E2xxx series (Conroe) with Dual Core technology up to E2160
Celeron 4xx series (Conroe) up to Celeron 440
It doesn't mention any quad core chips. You should contact the vendor for verification. Don't just buy it and expect it to work because it will physically fit in the socket.
Also I would rather go by the list I found than by what HP has to say. I once was on the phone with them for 4 hours bouncing of technician to technician and they could not fix my problem. 30 minutes chatting with my friend (who doesn't even have any type of schooling for computer repair) got it fixed.
@ malmental: I'm going to upgrade the Ram next, it has 2Gigs of ram and I'm running Vista so its a pain in the butt. After that I'm just going to get a nice hard drive and start saving up for a better build.
Hope it works. But I have had many OEM systems like Dell, HP, and Gateway. If their list says it doesn't work, that means their BIOS doesn't support it. I had a couple of HP and Dell laptops, says they only support broadcomm wifi chips, and it is true. I tried to upgrade the 802.11g cards to Atheros 802.11n with bluetooth. The system would not let me boot to windows. Just got a friendly message that the card is not supported in my system and it wouldn't boot any further. So even the hardware should physically fit and the chipset should physically run it, doesn't mean the BIOS will let you. Manufacturers love to lock their BIOS so you need them for support. They don't want you to change parts that they can't make money on.
That is why you should listen to the manufacturer website. This kind of thing is not guess work. BIOS limitations from HP are worse than hardware limitations. I hate to buy HP, Dell, Gateway or any of them because of their limitations. That is what got me started building PCs myself, LOL
BTW... back in the Pentium 3 and early Pentium 4 days... I killed 2 HP desktops and 1 laptop just because I added more RAM! After adding more RAM, it would just beep and memory error. I would have to unplug the BIOS battery and let it sit for 15 minutes and put the old sticks back in. Even if I used the same brand, same density and so on... just wouldn't work! After that, I started building all my PCs. Dell and Acer are more flexible than most. HP and Gateway or usually just plain picky!