Leo doesn't think this is a malware issue because it's not opening up any malicious sites, just the ones he was previously visiting. The first thing to try is resetting Internet Explorer in settings. Doing a full reset may clear out what was causing the problem.
Frank could also do a Windows System Restore to the point before this started happening.
Ultimately Leo suggests switching to Chrome. He believes it's a more secure browser, and Frank can even import all of his favorites from Internet Explorer to help him get started with it. If he doesn't like Chrome, he can always switch back to Internet Explorer again.
There were also some security issues with Java, so disabling Java may be a good idea too.