Macbook Pro 8,1 not charging
The battery on that MacBook Pro is dead. You could:


Have Apple replace the battery for you. However, since your laptop is most likely out of warranty after 6 years, this will cost you a pretty penny.
Buy a replacement battery and replace it yourself using these instructions from iFixit. The procedure is rated as easy and the page includes a video guide.
Use that laptop as a desktop replacement (permanently plugged-in). You’ll need to be extra careful to avoid data loss, considering the MagSafe connector will come unplugged very easily. You may consider duct-taping it in place.