wow, that sounds really weird. IT sounds as though something is wrong with the battery, like it's not keeping a charge.
I haven't come across a problem like this, and you said it came on randomly...which makes it even harder to troubleshoot.
There are a few options:
1. If your computer was plugged in when the power went off, there might have been a short circuit overloading and blowing some capacitors which are used mainly in the start-up process.
2. There might have been a small dust piece or something that has gotten in between the battery and the electric pins that the battery connects to.
3. your computer is just old.
The only one of those options you can check yourself is #2; for the others you would need to take it in to be repaired or replaced.