You could easily have other issues but I'm not sure about what else is going on with your computer. I'd probably get more RAM. For your 32 bit OS, I'd recommend having the 4GB max in there. If you're just looking for a new processor, Pentium G series or i3 are good affordable cpu's.
I doubt your processor has "slowed down" any. You probably have a lot of registry errors and junk files and other crap wasting resources. Try running CCleaner a couple times. Do the Clean and Registry portions both. http://www.piriform.com/ccleaner
It's free and it's safe. Most folks use it or a similar app regularly to keep their machines clean.
If you have acquired a lot of programs running at start up you don't need, that will also waste resources.
If you still want to upgrade your processor, let us know which motherboard you have. Or at the very least, which socket it has. The Pentium dual cores were available in several socket choices over the years.