Doesn't that mean that someone, likely RS or AK was there to turn on the computer? Doesn't that support their shared alibis that they were at RS' apt. in bed? Are you saying that they murdered Meredith, then went to RS' apt. to be there at 5:30 am, then went back to clean up the scene?
From 12:00 or whenever it was, until 5:30 am is a long time. I don't understand your question.