This is a list of the CPU's supported, pulled from here https://h10057.www1.hp.com/ecomcat/hpcatalog/specs/provisioner/05/AK818AW.htm:
A BIOS update may be necessary for some CPU's
The fastest you can get is a Q9300 (A Quad Core), or a E8500 (Dual Core)
Intel® Celeron® Processor 420 / 430 / 440 / 450 (1.60 to 2.20 GHz, 512 KB L2 cache, 800 MHz FSB) or Intel® Celeron® Dual Core Processor E1200 (1.60 GHz, 512 KB L2 cache, 800 MHz FSB) or Intel® Pentium® Dual Core Processor E2160 / E2180 / E2200 / E5200 / E5300 (1.80 to 2.60 GHz, 1 to 2 MB L2 cache, 800 MHz FSB) or Intel® Core™2 Duo Processor E4500 / E4600 / E6550 / E6750 / E7200 / E7300 / E7400 / E8200 / E8400 / E8500 (2.20 to 3.16 GHz, 2 to 6 MB L2 cache, 800 to 1333 MHz FSB) or Intel® Core™2 Quad Processor Q6600 / Q8200 / Q9300 (2.33 to 2.50 GHz, 4 to 8 MB L2 cache, 1066 to 1333 MHz FSB);
Ebay and Craigslist are good for used CPU's