Thanks
Ben for the great advice and info!!! No wonder the battery in this laptop is junk.....I thought maybe it had something to do with being a Compaq....but I now clearly see it's not the manufacturer creating the problem, it's the users (my daughter and I). Yikes!
This laptop has gotten HOT so many times before and no....not so much by me

I tend to have a little more respect for things that aren't mine and that aren't easily replaceable. But, I don't know how many times I've walked in daughter's room to get the laptop from her and she will have it lying right on her bed and blankets while she is using it! I've warned her about that until I'm blue in the face but what can I really do....it's her laptop?
So definitely the battery has never been put in the fridge....who would'a thought? But it makes sense because I've myself have stored batteries in the fridge, just not a laptop battery
Now in addressing your last tid-bit of excellent advice and my irritating issue....I have been doing the exact opposite in regards to the 20% and 80%. For some reason I thought letting the battery get as close to draining as possible (at which times would often completely drain if I wasn't paying attention) and then I'd plug it back in to give it a nice, "beyond-full" charge. I thought that's how it was supposed to be done...Oops!
So do you think this battery is shot or could it possibly be salvaged if I were to start caring for it in the way you advise above? Thanks again Ben for the awesome advice and information!