|Man would that ever be simple on a UNIX/Linux box!|
You could create a batchfile that runs the systeminfo command and pipes it into a text file. You would of course have it run at shutdown.
From there you would extract the one line and put it into a log file. However, what command to use to extract that line I don't know. Hopefully someone with much better batchfile skills than me will help you out.
If it were UNIX the command would be something like:
grep "System Up Time" [name_of_text_file] >> [name_of_log_file]