Your Sys Admin is fine with you doing this? He/she should be working to resolve, or at least be directing you to what to look for before simply power-down/power-up.
So many things to think about...
# users connected
memory space in-use/free
disk space free
last user connected; last program run
cron jobs
and so on.
As you look through, probably several will be quickly ruled out. However, a system should not freeze without a reason.