It's the battery. Be sure to check if the battery is heating up. This can be the sign a cell or two have shorted and this can stress the laptop power supply and cause yet another circuit failure.
I just had a inspiron 1150 given to me in pieces in a bag and my knowledge is very limited.
I work a lot on desktops and I've torn apart some old laptops just for the heck of it.
I found that the power plug was almost off on this motherboard.
I was able to unsolder it and clean it up and re-solder the part back in.
The laptop booted perfect with the power supply hooked up. I charged up the battery and restarted the laptop no problem.
When I let the laptop sit for a few minutes and it won't boot no lights or anything.
If I take the battery out and pop it back in the laptop will boot fine.
And sometimes it will say bios time is incorrect.
I thought BIOS battery but I don't know if there is a Bios battery.
The battery seam's to hold a poor charge about 1 hour.
So can this just be a bad battery or something in the battery connection inside this laptop?
Or something to do with the power connector I resoldered?
Thanks for reading this long winded post.