I think that he may be going for suicide. If they can get proof that she had written things about being depressed then manner of death can be suicide. If the things she wrote were happy and upbeat then the focus would be on homicide.
Or, if drugs were ordered online, who did the ordering, or under what name.
Maybe. And that's why HKS would leave all the bottles around and that wrapper of the suppository on the ground. To leave the impression of suicide perhaps? But who's to say who administered the last fatal dose of whatever.... Just like the suspicions surrounding Marilyn.
But we know he had her password and could have faked all sorts of things on there!
If it's the computer he's looking at, sounds like you're right. He's trying to rule it in or out, and I wonder if they've also looked to see if any drugs were ordered online? At first, I was thinking some of the additional evidence Perper mentioned might be something from Daniel's autopsy. Still could be, I suppose.