I always find it somewhat daunting when people say "will this work?" as unless somebody here has actually used it in the same configuration you are planning to, there is no real magic answer.
I have a HP Pavaillion a1730n.. it's just an AMD 4600+ Dual Core, 2GB Ram, 320GB Sata HD and SATA DVD, with onboard Nvidia GeForce 6150 LE Video and onboard 100Meg Network.
Works perfectly fine as a media director and ubuntu in general.
Mind you, I haven't used this as my core because I bought a barebones AMD 4600+ to do that (see my page in my signature). When I bought the HP it was $990 CDN just for the box (and guts), keyboard and mouse. About a year later when I went to buy the generic barebones box with the same CPU? It was around $300 (can't remember the exact price). I like the HP... it's super quiet too.
Quad Core is way more CPU than you'd need. 3 GB's of RAM is more than enough. Your main concern should be what video card and what network connections on that box.
As they say, your mileage may vary (but I think you have a good box there!)