No need to replace the PC, but adding some memory will help the PC a lot, I'm sure at your age your aware how valuable memory can get
Most of the anti-spyware applications out today a resource hungry, using fancy graphics skins and so forth (which I don't agree with myself- the app is supposed to clean the PC of infections, not look pretty!)- which is causing issues with your limited RAM.
I ran my old AMD 350Mhz K6-2 with 98SE and 32MB of RAM, and I got by just fine, but I couldn't believe the improvement when I upgraded to 256MB, and after that when I maxed it out to 512MB.
When I had 32MB of RAM, it was at a premium, so in general it';s best ot avoid running more then one or two "heavyweight" application at a time- Word, Excel, Internet Explorer, etc (pretty much any app, really)-
Additionally at the time the PC was not connected to the internet so I was relieved of the burden of a AV solution running in the background- in this case since you are on dial-up and need to connect to access the internet it should be safe for you to disable the background scanner of your antivirus (at least until you upgrade the RAM); as long as you are understandably cautious browsing the web, you should be fine.
failing anything else- I recommend acquiring a Windows 98SE CD, so that you may perform a clean install of your OS- (if we cannot find an alternate solution)- In the extreme case, you could actually go
back to windows 95; finding that will be harder then finding a 98SE CD, and both might be equal in price to a RAM upgrade, which would likely allow the PC to run the scans you are trying to run.
Trust me when I say I don't believe a computer can ever go obsolete; after all, the first IBM-PC was touted as being able to run word processors and spreadsheets; today's computers are used to run word processors and spreadsheets with fancy graphics, which is pretty much the difference- how adding a pretty menu or design to the interface makes the previous iteration obsolete seems like a specious claim
Sorry... I have a tendency to ramble about things...