you mention you have iMac G5 and OS 10.6.6, it's probably not a G5.
anyways, if you have wireless router, maybe somebody is connecting via your router?
there is a site that runs port scan,
http://www.grc.com/intro.htm
on top where it's says "Services" select ShieldsUP! and try the test, on the Mac it usually says the computer is "invisible" which is a good thing.