Macbook Pro 17 Won't Sleep.

I have a 2010 Macbook Pro 17" i7 model. Everything seems to work pretty well, but there is one issue. No matter what I do, the laptop will not sleep. If I click sleep/close the lid/press the power button, the computer just turns off instead of sleeping. I've tried resetting PRAM and SMC; no dice there. The battery says "Service Battery", so I was thinking that might be the problem, but getting a battery replaced is pricy. The issue happens regardless of if the charger is plugged in or not, but when the charger is plugged in it goes to green for a split second when the computer turns off, then back to orange. Is there any way this could be caused by a faulty logic board, or is it probably the battery?