Acer Aspire notebook stopped running off the mains, and will only run off the battery

I have an Acer Aspire 1670 that’s about a year and a half old. Basically what happens is that the machine stopped running off the mains, and will only run off the battery. The only way to charge the battery again is to turn the computer off, and then it will charge again. That began happening about 2 weeks ago. Then a few days ago the charging when turned off became really tempremental, and then it just stopped.
The power adapter says that power is getting from the mains to the adapter, but then the battery still won’t charge. Does anyone know what the problem could be?

I think it could be a bad DC jack. I do not work with Acer notebooks, so it would be only my guess. Try to plug in the AC adapter and wiggle the plug inside the jack. Can you make LEDs to flicker by wiggling the jack? Try to press on the power button while you are wiggling the power jack. If you notice that you can start the laptop when you apply some pressure on the power plug (and power jack), then most likely you have a power jack issue.
The problem you’ve described is very similar to a Toshiba Satellite A70 and A75 power jack problem. A crack occurs between the positive connector on the jack and the system board. As a result, the laptop battery charges only intermittently or doesn’t charge at all, the laptop will not run on AC power or the laptop will not turn on at all. Usually you can solve this problem by re-soldering or replacing the power jack on the system board.
I’m not sure if the power jack is a part of the system board on Acer Aspire 1670 laptop, so remember it’s just a guess.
I would also test the AC adapter itself. May be the adapter is bad even though an LED lights up.
Try to remove the battery and run the laptop just on AC power. Does it make any difference? Can you turn it on?