Maybe what was ON the computer changed it... like with Scott Peterson, when he was researching tides in the bay he dumped Lacy's body in. Many times criminals research how-to and these days those traces don't disappear. Could be HKS was counting on everyone assuming accidental death and never having this computer looked at.
Or like if someone put in "blue lips" in google at 10:30AM.
Do we know for sure it was HIS computer. The computer was referred to as "a computer that was in the room". Now this was a suite. Perhaps the suite came with an in-room laptop. In which case, HKS could do nothing about it.
What if what was on the computer was not something HKS was doing, but what Anna was doing? What if she sent something out to someone that she was being held captive?
Even a caveman knows not to use your computer for research before you murder someone. He's a stupid criminal, but not so stupid to assume their would be no investigation into his and hers computers.