I have a website that has been stopped and trying to figure out how long it has been down and if it was shutdown intentionally or not.
The short answer for the outage duration part is "not a GOOD way..." -- what you really need is a monitoring system that tells you when your server is down (and when it comes back up again).
In the absence of a monitoring system you can use log files (when did the access log stop? When did it start showing activity again?), file access/change dates (logs, timestamps on uploaded files, etc.) to approximate things.
For the cause, your server's logs should also show if the shutdown was intentional (orderly shutdown initiated by a user) or unintentional/unclean (some kind of crash error message).