This sounds obvious, but did you check the power supply (for being clogged)
and is it big enough for what you need? As our needs grow it sometimes means
we need a bigger power supply. Maxing it out over a periods of time can
cause freezing. If you have a spare power supply then you could see if it
makes a difference. Given the random nature it is something to consider.

If power supply checks out OK and you plan on continue using Ubuntu you need
to backup versions to may be 9.10 or 9.04 or so. Or try another Linux disto.

This is strange. My advice is to boot up a live CD and see what happens. I
would try Knoppix, Puppy, Mepia and Ubuntu, one after another.
But the first thing would be to try another DE or WM. Why not login into
xterm, install something fast and reliable and try it ?

Oh yes that is the first fan to be cleaned up and yes it is large enough
for this MB. I do not have a power tester but may get one sometime.

Well, that is one variable to rule out. I've got to admit that it is
confusing. You might want to ask a question here: http://askubuntu.com/

Some big names in Ubuntu actually answer your questions along with other
users. People are rated on their responses and it gives them more authority.

What about "brownouts"? If you live in NYC this might be the cause. I have
noticed my small CD player and fan behaving strangely because of them. Even may
have bought an unneed CD Player replacement because of them. Was worried I'd
have to replace the room fan but then attributed the problem to "brownouts".

Try hooking in a UPS.

I do not live in the USA but we have power surges that we need a surge
protector for and I have them.

A surge protector is not the same as a UPS, it will not protect you against
drops in power, "brownouts". The UPS has a battery system that maintains power
during drops or blackouts for hopefully enough time to close a file and back up
your work.

Not interested because it does not bother me if the power drops only if
it surges and blows my computers, TVs etc' I did know what UPS means.

Power supplies have low voltage sensors. Without any other monitoring
your power supply if working properly will shut down. Another story
however on the output supply. Many power supplies in cut rate computers
are specked out to small for the hardware in the box. To trouble shoot
you may disconnect extra drives and should see positive results.

If in fact the box shuts down while booted up an improper shut down of
the system may cause problems with the OS.

You can also have a faulty card that is drawing to much power. Trying to
trouble shoot, remove the extra cards that may be installed, one at a
time, then reinstall them to look for a difference. If you find a bad
card or drive replace it because a new power supply will not fix the
problem. A UPS will not fix an internal problem. One can monitor the
voltage and if it dips when problems occur this would be a good avenue
to take.

For the record. An OS relies on proper running hardware, it is not a
cure for a bad hardware.