I'm having trouble with your statement that a hard power cycle was
needed to close firefox. If an app in linux can't be killed, then there
is something else going on - bad RAM, overheating perhaps? I would try
logging into the machine via secure shell and taking a look, before
taking such a drastic step.

The kde corruption is most likely the result of the unclean shutdown.
kde is not known for great stability, at least not since the days of kde
3.5.x, so the easiest fix is probably just to remove the kde config
files from your home directory. (I'm guessing.kde* and/or .qt* - but
it's been a few years since I've used kde)

You can verify that the problem is corrupt kde config files by creating
a new account on the machine, then logging in and starting a kde session
under the new account.