My Aspire z5700 keeps shutting itself down - questions

Hello, I purchased my aspire Z5700 back in the summer of 2010, and it's been great. However, lately (this started a couple days ago), the computer shuts itself down.

At first I thought perhaps it was the fan, and so I downloaded Speccy to monitor the temperatures and lowered the heat in the room and that seemed to be okay.

But then it started happening again. I thought maybe it's the wire, so I'd remove the power cord and then replug it back in, as that was the only way to turn the computer back on. And it seemed to have worked for a bit

But then today it's having problems and the last time it shut itself off, when I turned on the computer again, the computer had set the date back to 2010, and according to various articles on google, this can mean the battery is having issues.

Another time when I turned the computer back, Norton said I needed to verify my subscription but then said I was fine?

I also did several virus scans but nothing.

My questions are this:
1.) Has anyone else with an apsire z7500 experience this after 4-5 years?
2.) Does anyone know the price for a replacement battery (assuming that's it). I am seeing what makes more sense financially (if this is the problem). To buy a new battery or just get a new computer
3.) Does anyone have any ideas of what else it might be?

Any help is much appreciated. I'm a geek who spends a lot of time on my computer and would be sad by not having a functioning one to use lol

Thanks! -Michele