Just to kick into this one, on older computers I'd highly recommend Microsoft Security Essentials. It's very light on resource so doesn't slow your machine down at all.

It may have weaknesses in that it's made by the people who made the un-safe operating system but unless you download things from torrents or go on naughty websites it'll cover you.

The other thing to recommend whenever this happens is a program called Malware Bytes Anti Malware. It's not an antivirus, but it's a virus scanner and will remove pretty much any nasty you come across. So use MSE as your day-to-day "let it do it's thing" AV, and then run MBAM when you think you might have caught something, or just once a month or so.

So many people buy new computers when all they need is a bit of maintenance, so you're always better off asking some techies before ditching a slow machine.