The specs for the motherboard used in this computer are here
. It's a socket 939 board, which is outdated now and there aren't a lot of processors available. Here's one
, but it doesn't get the 2.5 GHz speed you want. So the answer is yes, you can install a dual-core processor, but you probably shouldn't.
You would be better off to replace both the motherboard and processor together so you can pick from current processors. Here is
a typical combo offer with a 3.0 GHz dual-core that is only about $20 more than the processor linked to above.
The downside to upgrading this way is that you normally can't stop with just the motherboard and processor. Your current memory won't fit on the new board, so that'll need to be replaced. Then you'll need to replace the power supply as well. The supplies used in machines like this Presario don't offer the capacity the new board and processor need for stable operation. And finally, if you're an avid gamer, the built-in video is usually inadequate. You'll be looking at a new video card too.
At least the case and peripherals would still be useable, so you can put all your new parts into your current box. Unless you want something flashier to go with all the new innards. You'll also need to reinstall Windows, since the current installation probably won't run on the new system. A fresh installation would be the fastest way to get up and running. This means hunting up a Windows CD for the version currently running; at least you can reuse your product key, although you'll almost certainly wind up activating Windows over the phone. (My experience has been that when using the OEM key with such a new system, the Internet activation usually fails. The automated phone system asks you how many computers you're running this copy on, so you can just answer "one", which is the truth.)
Maybe not what you wanted to hear, but this is the way to get a machine that will do what you are looking for. Thanks for using Fixya!