Sony+battery life

Defective battery, or something draining it. Try cycling the batteries by allowing the computer to run off the battery until it powers off, this will completely drain the batteries (be sure to turn off any power saving functions) then recharge the battery till full....do this about three times and see if the battery life is any better. If it is then great, if not contact manufacturer about replacing the battery.

Most batteries have a 1 yr warranty, even if the laptop has a longer one. Batteries tend to die or come close to it after about 3 years. If the battery only lasts as little as you say, the charging method above will not work to fix it. That should be done once in a while during the usefull life of the battery to prolong it's life (also not leaving the laptop plugged in all the time with the battery in), not to shock it back to life. You're probably looking at a new battery purchase.

Cheap ebay China battery is about 1/3 the cost of an OEM Sony battery, but also has 1/3 the life span. They tend to drop down after just a few months of use, no matter how many times they say "OEM Quality" in the sale.

This is probably a case of dead battery, how old is it?
You might need to purchase a new one...