I was ready to take the machine apart, now I’m glad I didn’t.
Most likely there is nothing wrong with the adapter but just in case test it with a voltmeter to make sure the output voltage is correct. Unplug the AC adapter, remove the battery and wait for 1-2 minutes. Try reseating the memory module, just remove it from the slot on the motherboard and install it back.
The output amperage has to be the same as on the original adapter or higher, but not lower.
When you plug the AC adapter the power LED and the battery charge LED light up.
About 15-20% of all Toshiba laptops we get for repair, suffer from an overheating problem. This is one of the most common problems with Toshiba laptops we deal with.
Solution: If the CPU heatsink is not clogged with dust and lint completely, you can use canned air and just blow it inside the laptop through the openings on the bottom and on the sides.