Freezing up to the extent that a forced shut down is needed is the
main issue here and it's possible that the Hard Drive has been
corrupted through these forced power removals.

For future reference, if the Hard Drive activity light is flickering
then the PC is still alive even if the mouse cursor is stuck. One test
is to press the Caps Lock to see if the light toggles on/off - if it
does then the keyboard is live so you can use [CTRL]+[ALT]+[DEL] to
bring up the proper log-off / power down screen, or use the RSEIUB key
sequence if that fails. Lots of tips on what can be done with a system
that looks dead but really isn't here:

http://en.wikipedia.org/wiki/Magic_SysRq_key

Ubuntu usually will run a file check on startup if it detects this,
and will also force a check every 30 boots, so do you see this
happening when you start up the system ?

You can try using a Live CD and checking the file system with that,
plus see what it can detect on the Hard Drive. I like to use 9.10 as
that allows viewing the SMART data without installing and have it on a
USB drive as well as CD for those system that won't boot from USB

Not "the" answer, just a first reaction from a self-considered novice:

I'd think that your file system may have become corrupted. This would
explain both the freezing and the loss of files.
As a cause of file system corruption I could imagine loss of power
before any buffers could have been flushed.

I'm ready to stand corrected and learn about both the cause and the
solution!

Do you have /home in a separate partition? Sure you are logged into the
right user account?

I frequently get freezes with the mouse, so I always try control+alt+delete and
control+alt+backspace, then I shutoff. Luckily, either the Hiren's tools or Mint
Linux LXDE autochecks the hard drive once in awhile. Why do I mention
Hiren's...because this HP laptop doesn't support booting from USB external hard
drive.
The Puppy Live CD based off Ubuntu used to fix unclean shutoffs, but I haven't
tried it on any Linux expect Ubuntu 10.04. I had the power go out while updating
once.