This is not an issue with the OS. The notebook is suppose to charge even
if the unit is simply plugged it, not even booted. It sounds like you
have a hardware issue with the connections to the battery.

The laptop is a sony vaio pcg-frv27. I already replaced the harddrive.
It seems if I go into the power management options and change the turn
off if battery power is critical option i can run it on the battery.
As soon as I change that back to shutdown or suspend if power is
critical when I switch to battery it shuts down.

When was the last time the BIOS was updated on the LT? I believe the Sony's has
an BIOS that is updated here and there. I seen this topic before on Ubuntu
forums. Thus there is going to be a slight challenge to update with Linux O/S on
the HD. I think once you get the BIOS updated, the problem should go away.

Unfortunately I am not sure how to update the bios. Sony has this wierd
program that runs in windows to update the bios. Since the laptop only runs
ubuntu I am not sure how to make it work. I asked sony if they had a version
that I could do in dos or even a linux version and they said no to both
questions and said they didnt have any plans on changing it so I am just
stuck. Made me want to get a new laptop but 26 year old male on ssi cant get
financing nor can I afford to buy a new one strait out. If anyone can figure
out how to make the bios update program work in ubuntu I would be very very
grateful.

ubuntuforums.org/showthread.php+BIOS
ubuntuforums.org/showthread.php+BIOS
This is some thing that you can post on the Ubie forum. I recommend ubies
forums.

What is the model of your LT? It may be a HD issue, but it will not hurt to
check if there is a know bug.