I don't have a definitive answer, but since posting a similar question today I have found that this issue is related to a failing screen. I also found Apple will replace, not repair, with another Gen 2 for $109.00 plus shipping. Can buy newest model for not much more. You can buy a new screen here, around $30.00, but the repair is rated as difficult.
At the age of this item the battery will be in need of replacement soon, the battery is connected to screen, makes sense to replace both in this case. I guess the question is, buy new or experiment replacing battery and screen. May save $50.00, may not.
Never, ever approach a computer saying or even thinking "I will just do this quickly".