Unable to keep applications open

Dell XPS 600, P-III, 768 mb RAM, Win XP HE (SP1) (upgrade from Win98se) dial-up connection.
I am trying to troubleshoot my Dad?s computer, it boots ok however when you attempt to open IE 6, the homepage appears momentarily then disappears. The same thing happens when I try to open control panel, dial up connection and other programs. The computer appears to ?mini-boot? i.e. all icons and the task-bar disappear then re-appear as if rebooting. This started after a grandson was surfing (porno sites) the internet. I performed a virus scan (NAV corporate edition) found a couple of Trojans; disabled sys restore, deleted the virus and rebooted. Rescanned and found no more virus but the problem still exists. Any ideas where else to check. I am not a tech but I am fairly comfortable working on my own computers. Thanks to all
I posted this on Computer Help and was advised to repost on security, I will try the stinger program and advise the results. Thanks again