if you use it only on the battery does it work ?
No. I have two identical 5315's. The broken one has a very poor battery. So, I put the decent battery into the broken laptop, made sure the power plug was out, and pressed the On button. Nothing. No lights (specifically no green light on the left). There are two small LED lights. The left one has an icon near it, like a light bulb. The right one has a icon showing a battery.
On the good laptop, when I attach the DC power plug, the right hand LED (battery icon) lights up amber. When I switch the laptop on, the left LED (light bulb icon) shows green.
On the bad laptop, no LED lights up in any circumstances.
EDIT1: The amber light eventually turns green. So, on a laptop with a charged battery, two green lights would show.