Hi!

It would be worthwhile to examine the power brick or the connector for it on
the computer to see if either one has failed. It sounds like you're losing
power input to the computer and it switches over to the battery as a result.
If it were to happen enough, this could make charging the battery a very
lengthy proposition. You might get lucky and find a bad line cord (most are
detachable and therefore easily/cheaply replaced), frayed wire on the output
side of the "brick" or a dirty connector.

William