All that happens on your computer is Logged in Event Logs.
Operating System records the system startup and shutdown times and logs them in the event log with the following Event IDs:
• Event 6005 is logged at boot time noting that the Event Log service was started. It gives the message "The Event log service was started".
• Event 6006 is logged as a clean shutdown. It gives the message "The Event log service was stopped".
• Event 6008 is logged as a dirty shutdown. It gives the message "The previous system shutdown at time on date was unexpected".
So just filter these events out and you can find out when the system started and when it was shut down etc ...
BTW it has whole lot more information just in case you are interested browse through the events