The first question is: how do you know KDE is crashing? It may be clear that something crashed, but it also can be X or the kernel. Therefor, there are a couple of thing you can look for.
- Does the led's on the keyboard light up and flikker.
- Can you enter the computer from another computer in the network (if available).
If (1) occures, the kernel is possible crashed; if (2) occures the kernel is certainly not crashes. After you made a connection with (2) you can search for what the computer is doing, or shutdown it properly.
After that, you can search your log files for more information about what happened. For a problem with X or KDE,
~/.xsession-errors is the first log to investigate, elsewise you can look for errors in
/var/log/messages or some else log in that directory.
Crashes can be caused by many different causes, and there are many ways a program can crash. For example, bad hardware also can cause random crashes.