Guardian:I am hesitant to touch this, as it is an OEM PC, and they tend to do screwy things with hardware.
The motherboard under the hood is an Asus P5LP-LE, but there is a very real possibility that it is a locked down version that will only work with a limited number of processors.
It comes with a Pentium D that has a FSB (front side bus) of 800 MHz, so if you can find anything that fits those two criteria you should be safe. Beyond that, it's anybody's guess.
Is there any perticular reason you want a new processor for this machine?
Honestly, you would probably better off saving for just a little bit longer and getting a new motherboard/processor (the egg often has combo deals for stuff like that) and a new case. The cost really wouldn't be much over what you are able to spend now, anyway, and you'd have a more open platform that you can build off of in the future (plus, a much better platform for gaming).
The Asus P5LP-LE motherboard comes with an Intel 945P chipset. I've never seen an OEM motherboard actually limit the kind of CPU you can install via the BIOS. Limitations are usually based on the generation of the motherboard. The 945P chipset supports the Intel Pentium D (800 and 900 series), Intel Pentium 4, and the 65nm Intel Core 2 Duo CPUs (E6400, E6600, E6700, X6800) which have an FSB of 1066. The 2nd generation 65nm processors with a 1333mhz FSB such as the E6750 and E6850 will not work on this motherboard.
However, it might be a bit difficult for you to find the mentioned supported processors at decent prices, since they would be now over 2 years old. I would recommend buying a low end mATX motherboard, an E7200, and 2GB of DDR2-800 RAM as an upgrade solution. This should cost you around $200.
Let me know if you'd like to go that route and I can offer you some suggestions as to specific hardware.
Core 2 Duo E6600 @ 3.33GHz w/ Silverstone Nitrogon NT06 (both lapped)
ATI Radeon HD 4850 @ 690/1150
ASUS P5K-E WiFi/AP Edition, 4GB DDR2-800
Lian Li PC-7B w/ 2 Silverstone FM-121 + 1 FM-81
LSI MegaRAID 320-2 w/ 18GB 15k, 74GB 15k, 2x150GB 10k RAID 1 (SCSI drives), 500GB SATA
Creative X-Fi Platinum
Enermax Aurora, Logitech MX1000
Envision EN2028 20" 1600x1200 + Samsung 710N 17"
Yamaha HTR-5940, 5x PolkAudio Monitor 40 bi-wired with 12AWG, PolkAudio CS1, Klipsch Sub10, Optical from X-Fi