How do you remove all traces of a spyware program such as Limewire from your computer?

I have a second hand computer that had Limewire on it when I bought it. I took little notice of it until the other day it requested internet access to update itself. I declined, where upon it threw a fit and kept asking over and over. Every time I shut it down, it reopened. Then my computer almost completely... show more I have a second hand computer that had Limewire on it when I bought it. I took little notice of it until the other day it requested internet access to update itself. I declined, where upon it threw a fit and kept asking over and over. Every time I shut it down, it reopened. Then my computer almost completely stopped working - every time I pressed a button it would take up to 10 minutes to respond. So I block Limewire from the net with my firewall and my computer started working again. I uninstalled Limewire but kept getting error messages telling me to reinstall...they were popping up continuously.

So I did a search on my computer and deleted everything with Limewire in the title and the error messages stopped.

How can I be sure it's really gone?
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