Can bad battery cause power issues?

I have a MacBook Pro 15" Core 2 Duo Model A1260 2.4. Can a failing battery cause the backlight for the keyboard to not work on a A1260 macbook pro? The caps lock light works but the keyboard no longer lights up and I am getting a service battery warning. I also have been noticing issues with performance even though I have the 85w adapter plugged in at all times. The logic board was replaced less then a year ago, and the battery a little over a year ago, bought it used, so I am replacing it. I just want to know if the culprit could be something else and if so, what could it be?