You could try 10.10 and perhaps a closely related distro like Mint.

That was my initial thought as well, I tried Debian 5
but can't install libusb-1.0-1. I also tried the Debian 6 squeeze RC1,
which works and the tether connects, but I get the same issue with the
computer shutting itself off after 10-15 min.

I'll try Mint and 10.10, not going to happen this weekend though...

Maybe using a Puppy Linux Live CD or other up-to-date Live CD to get on the Web
and save stuff to either USB or mount and transfer files to Xubuntu, remember to
un-mount. I do this Windows computers, I have to work on all the time, plus to
back-up my Linux computers.

It shutting off after 10-15 minutes sounds to me like a heat problem caused
by the fan not working and/or dust preventing the CPU from being cooled
properly. Do a Google search and see if you can find instructions on
disassembling the laptop and checking the fan and dust level and blowing it
out. Several years ago I had a fan lock-up on me, I sure some use the
cheapest bearings they can find because 2 years out its your problem, and
had to replace it.

I had an ACER netbook system board go out on me last summer. The replacement
was more than the computer was worth. Fortunately I found instructions on
Google on how to disassemble it. I removed the HD and placed it in a Kingwin
SATA external enclosure so all the goodies we are suppose to keep backed up
and don't was recovered.

I have had a lot of trouble running later versions of Ubuntu on older hardware.
Before installing this distro, try running the LiveCD to see if it works or not.

I run 10.04 on an older less powerful computer without any problems

Well, I was convinced it couldn't be the fan because I could see the fan
spinning on the bottom of the computer and it looked pretty clean, but I
decided I had to take the thing apart anyway. There was some dust buildup
but nothing that would have choked the fan off. There were however 2 fans,
one of which wasn't working. I took the heat sink/fan assy off and cleaned
it out, and while I was at it, I stuck a thin copper shim between the heat
sink and cpu. I tried this on a hp dv9000 after reflowing the solder on the
video chip with a cheap heat gun and a cheaper infrared thermometer and it
has worked great. While putting the thing back together, I wriggled the
power connections from the fans to the main board and lo and behold, the
second fan started blowing. Still running Debian Squeeze but, I'm going to
try getting Ubuntu or Xubuntu 10.04 going in the morning. Now I just have
to figure out what to do with these extra screws...

It sure is a learning curve once inside the box !!!

No kidding. Sony doesn't publish their manuals, so I must have taken every
screw out trying to get to the fan(s) and it turned out to be just 1 screw and a
sideways push on the speaker panel, then 1 screw for the keyboard. I haven't
been able to get 10.04 on it yet, its locking up on a black screen even before
the main menu/language selection.