How do you know the AC power transformer is good? Did you stick the leads of a voltmeter into it to see that it is indeed passing current?
From what you describe, I'd suspect either a bad battery, bad power supply, or a bad power transformer/brick. If the machine is still under warranty, then make a claim. Otherwise, get a few estimates on the repair costs and weigh that against what it costs for a whole new laptop.
You can always get a $20US or so external enclosure for the old hard drive to access the data on it. I doubt there's anything wrong with the hard drive. Then you could sell the old unit on ebay for parts.
As a parting note, let this be a lesson about the value of making backups. You're getting off relatively easy compared to most people. ALWAYS, ALWAYS, ALWAYS have backups of important files or be prepared to lose them some day.
I was using my laptop recently, I went away for a few minutes and when I came back it was totally dead. I haven't been able to turn it on since! The AC lead is fine.
Is it possible that I have to get a new motherboard? If so, where could I get one?
By the way, my laptop is a Toshiba A110. It's just over a year old!
Please help! All my family photos are in this computer!