The battery indicator flashing when plugged in to electrical plug means your battery is completely dead and won't charge. You're computer should run with just the power cord. Your power cord most likely needs replacement.

If you know anyone with the same model of laptop ask if you can borrow their power cord and/or battery to test it out. It is rare for the problem to be the motherboard, though it does happen.

It may just be the power cord at fault as the computer should run without the battery, so you should replace the power cord, as it is probably the reason the battery is completely dead.

If the battery is at least a year old I would replace it since they generally don't last too much longer than a year.