Dell battery problem

A friend at work has a dell laptop, and it won't charge the battery. From what she says, it won't even turn on now, even when plugged in. It will start to, then shut off. I loaned her a spare battery, and she installed it, hit the power button, the lights flashed, stopped, and nothing.
Is there an easy way to tell if it's a battery problem, or a mother board problem?
I know mine are getting old, as both of them show "not recognized", but still will charge to a point and gives me an hour of power anyway.
I put her's in, and it showed 0 charge, and finally charged up to "2" hours left when removing the power cord.
Not knowing anything about this, is it hard to replace a mother board? I tried on a Toshiba once, and it now resides in the trash.
I guess it could also the the power jack, or even her charger... she says she's bringing it to work so I can look at it, but still waiting.
Just need to know what steps to do to make a better guess as to the problem.

 

I just used my charger, and it does the same thing. I did notice the rear of the CPU section is busted on both sides, like the lid has been opened and did not want to swivel.
I installed a charged battery and got it to stay on, and all she needs is to retrieve pictures she had stored on the hard drive, which I was going to try and do, but she forgot to tell me the password, so I guess it will have to wait.
Thanks for the help.