Hey bro, yes you can upgrade it, all you need is to make sure you have a dual core system, in which you do, and it will run 64 bit. All 32 bit system will only see and use 3gb of ram, so even if you have 4gb, windows will only see 3gb of it etc. If you add a 64 bit system then it will see exactly what ram you have, your motherboard probably only supports up to about 8gb or maybe 16gb as it seems to be a few years old most likely.
If you are hitting performance issues now, I would look at just purchasing a new server, and then transfer everything over to the new one. You can't upgrade from a 32 but to 64 bit, it's a clean install only, so you would have to backup everything and then restore your data etc. If you go the clean install, I would suggest that you buy a new hard drive, pull the old one out, put the new one in, then do your install.... after it's up and running, shut it down, plug in the old drive and it will mount as D:. Then you can copy over all your old data with ease, and have a backup drive built into the system.
If you do this yourself and need some help, just give me a call and we can pretty much do it all over the phone.