That's a lot of damage from just disconnecting the power - the Linux
file system is far more robust than that and shouldn't have been so
severely affected !

So, when you accidentally kicked out the power cable did you also
knock the tower case too ? The sort of things that are happening are
more indicative of HD or RAM problems - perhaps just a dislodged cable
or RAM stick or perhaps a head crash in the HD ( bad news ).

It looks like you are in for a clean install but you should be able to
get your data off by booting up with the Live CD and accessing the HD
contents. If you cannot mount the HD due to file system errors you can
run error correction using [ System / Administration / Disc Utility ].

Might be worthwhile checking inside the tower first, re-seat the RAM
and HD cables.

PS - [ System / Administration / GParted ] is the partition manager
and if you don't see this when booted into the Live CD you can install
it from the Ubuntu Software Center, though it won't be a permanent
change of course