I have a sony Vaio VPCSB 26FG laptop.
The laptop just switched off one day while it was on battery power and couldn't be turned on.
If I plugged in the charger, the computer would turn on, but the battery charge monitor would always say that the battery was 75% charged no more and no less.
When I pulled out the charger plug, the computer would die promptly, and could only be rebooted with the charger plugged in, it wouldn't work off the battery alone.
So I did a little searching around to try to solve the problem and read all the horrific stories on this forum about people taking dremels to their laptops, and pulling boards out etc etc.
Ok my solution was very simple, here goes:
On page 18 of the manual you'll see a diagram:
1. Turn off your laptop and flip it over so you can see the underside
2. find the "Battery Off" botton  on page 18 of the service manual
(it's a tiny hole right above the bottom cover and to the right of the Extended battery pack connector cover )
3. get a paper clip and insert the end into the hole, as you push you'll hear a click. Hold the button in for about 3 seconds and release
4. Now try booting up without the AC adapter
It worked for me, no dremels, or having to open up the computer or reinstall the bios.
Ok, if this doesn't work then the manual tells you to remove the battery and reseat it. Barring that, I guess more trouble shooting is in order.
There was a comment on about page 2 of this forum about pulling out the battery with the AC adapter plugged in / turned on and leaving the battery out for 5 minutes. This is possibly another thing to try if all else fails.
Hope this helps some people out there.
I have to say it looks like this is a major problem with Vaio laptops which Sony doesn't seem to care about fixing, and must bring them in a screed of revenue because so many people will buy new batteries.
All I can say is wouldn't touch a Sony Vaio again, and I will be getting a laptop for my kids soon, so I'll be looking for something a little more reliable.