A couple of questions based on what I'd look at if it was my computer...
- What is the event id of the logon event logs you're seeing?
- What is the logon type for the logins? (click the detail tab on the event log)
- Did you confirm your user account was the one that logged on? (click on the detail tab and expand the "system" section)
- What is the "logonprocessname" (click on the detail tab and expand the "system" section)
- Are you sure the machine was 100% powered off, not just asleep or hibernating (or transitioning from asleep to hibernating--e.g. laptop lid closed)? We've seen random logon events in the middle of the night (on corp network) when the computer was moving between the two states. I'm asking b/c there is a difference between a boot event log, and a Windows logon event log.
- What were the most recent boot and/or shutdown events near the logons (http://www.howtogeek.com/72420/how-to-use-event-viewer-to-find-your-pcs-boot-time/)
- Have you checked the bios for any sort of scheduled boot-up settings (e.g. "resume by alarm")?
- Are there any process creation events just before or during this time period (event 4688)?
For the process creation events, and for the events Didier mentioned and for process creation events, if this is a work computer, is it part of a domain with group policy enabled/applied? If so, you may have to confirm that these specific event logs are enabled. I don't know about the system time event logs referenced above, but I know that we weren't logging 4688 events until I asked the domain admin to enable them.