A few initial suggestions:
1. Check /var/log/syslog
2. A lot of system hangs experienced at the user level (i.e. in a desktop-use scenario) have to do with X hanging, not the base system "underneath" X. If it happens again, do a Ctrl + F1, log in as root, and run top. See if one of the apps you're running is hogging the CPU. This happens all too often with apps like firefox. If so, you can kill it with ps aux to get the PID, then kill -that PID- to get rid of it.
3. If you haven't backed up recently, do so. It could be that your hard drive is heading south, and we all know how fast that can happen!
In terms of how to know if it was an intrusion...that's a lot more difficult. If you're just running a linux desktop, it's very, very unlikely that someone somehow logged in to your machine remotely and then just made it stop responding. After all, even if someone *wanted* to take over your machine, they would *use* it for something, right? The only clues would be the logs (in /var/log again.)