Strike one--Using a forum to add to your woes of a cheating girl friend
Strike two--If she shuts down her computer quickly and won't grant you access--trust issues
Strike three--Man up and make a move. Either you're with her or you're cutting ties.
I know it's not always that simple but if you have no children, no co-homeownership or other major ventures, call it quits. If you have doubts now about her, you'll have them down the road after you're married with kids.
Trust is easily broken and rarely ever mended/fixed. If you ask her if she's cheating--she's not required to tell the truth. Sounds as if you need to cut your losses ahead of time. Just my .02 hanging out on a forum.