I sure can. Click start, right click on computer, click manage. This is the computer management console. On the left, there is a list, one of the first entries should be event viewer. Expand it, then expand Windows Logs, and click on System.
The viewer will load your system logs into the middle panel. You now want to filter out the regular run of the mill stuff, so click on filter in the right panel.
Filter current log -> Check mark Critical, Error, and Warnings, hit ok.
Now you're looking at what I was asking for. If you've been having to force shutdown your computer because it is hanging, it will show up here an an error, power removed from kernel. You are looking for any entry directly below this kernel power error, as the list goes newest to oldest.
So check the times, and try to see if there is an error here that corrisponds with a shutdown issue, before the power down. Depending on the error it may give an indication of why this problem could be happening.