Why does my laptop only work/turn on when it's on the charger?

I am hoping there is someone who can help me figure out why my laptop will not turn on/stay on unless it is on the charger. As soon as I unplug the charger from it, it automatically shuts off and I can not turn it back on unless I plug it back in, yet it keeps saying that it is "plugged in, not charging." This started happening a couple nights ago, and it would always stay at the same battery percentage, too; 87% to be exact; hours could go by and that "87%" would not change; it took almost 2 days for it to go down to 86%, where it currently is. I have tried figuring it out, but I seem to have no luck. It's a Lenovo Thinkpad laptop R500, if that helps anyone; it's not actually mine; I use it for school; that being said, I can't let this thing break, so if anyone has any idea what might be wrong and what I can do to solve it, please help me out.