Hi, and welcome to the forum!
You probably need a new case indeed... the HP case might be mATX, although not sure about that.
I would get a good Intel P965 Express based motherboard. They overclock very well, and are Core 2 Duo ready (some even Core 2 Quad) Some examples:
$115.99 - good budget board, no RAID on southbridge, only on secondary controller on the PCI-E Bus.
$142.99 - same as the S3, but better components (solid capacitators). Same issue with RAID.
$157.99 - good board
ASUS P5B Deluxe
$194.99 - very good board, with excellent overclocking results.
I am pretty certain the ASUS boards will support Core 2 Quad, but not too sure about the Gigabytes. What I ahve heard, only rev.2 of the Gigabyte boards support the Core 2 Quad. My personal pick would be one of the Asus boards.
If you want Crossfire or SLI, get an Intel 975X based board, like the Asus P5W DH Deluxe.