Asus 1215B won't stay on - Sudden Hard Shut Downs

Hello all!
A few years ago, this netbook died suddenly. I was browsing the net, the fan started to rev up extremely, and out of the blue, it instantly shut down (no "Powering off" message, just a hard power off). As soon as I started it, it would turn off. I thought it had to be something related to overheating, so I opened it up. Reseated everything, checked for dust and debris, applied some thermal paste and tightened everything back. The laptop runs cooler now, and I'm finally able to access the OS (at least for some minutes), but the sudden shut down issue persists, with the fan still revving up big time before the laptop dies. Sometimes, it hits as soon as the BIOS splash screen appears, sometimes after a good 20 minutes in the desktop.
Also, the battery won't charge, and the battery indicator blinks orange. I'm forced to use AC all the time.

Any suggestions regarding this matter? In case I'm in need of replacements, any trusted/recommended place to buy them?

Thanks in advance!