Well, I'm fairly familiar with the Dimensions 2XXX-4XXX Series of computers as my parents used to have one. I even have a 2400 I just refurbished sitting downstairs as I type this. I work on them all the time. I've always thought that they weren't the fastest computer, even after a fresh install it's quite noticeable that it's not a very speedy system.
So what I"m getting at is that you can't make slow... fast. See? It's quite possible that you are having internet connectivity issues, but that really isn't my area of expertise. You could try starting a topic in the networking forum
However, you mentioned earlier that the motherboards caps are starting to go. If they are swollen and/or bleeding, it's just a matter of time before it doesn't turn on one day. If you are very very strapped for money, and cannot afford a new PC, then looking at a site like Craigslist locally might be an option. That's actually what I do (sell used computers on Craigslist).
In my area, you can find some decent P4 2+ghz Hyper-Threading, 512mb RAM, 80gb HDD, XP Pro, CDRW for about $130-$150 or so. Look for guys like me that do it as a side business and it will come with a fresh install of the OS, all ready to go.
I still say build yourself a new computer, but that's an option.