On the actual battery (at the bottom of the computer) there should be a buttton and four led-lamps. Press that button, does any of the leds light up?
Either the battery is dead or the battery just need to be recalibrated (or the CMOS battery need a reset). There's a few other things to try too, like pressing the PMU-button for a few secs (while the computer is turned off) and start the computer again. Another is to reset the nvram, then you need to get into the Open Firmware.
To recalibrate the battery (but this means the battery needs to take some charge). Let the computer run down the battery so it goes to sleep by itself, charge the battery fully again and then let it run down another time and charge it back up.
The PMU-button should be under the keyboard, in the upper right corner (not sure on that model, but on mine it's a metalic button that you reach from a kidney shaped hole near the Power button).
To reset the CMOS battery take out the battery, remove the cords (power, USB, Firewire etc) from the computer. Let it sit for maybe 15 minutes then put the battery back, the cords etc.
To get into the Open Firmware you hold down the keys cmd-option-O-F until a gray screen shows up (this is when you power up the computer). Then type:
reset-nvram
reset-all
(the last command should reboot the machine and it should start into OS X as normal).
The last three things can be done all in a row, like press the PMU-button for a few seconds, then remove the battery etc to reset the CMOS battery and then reset the nvram in Open Firmware.
If nothing of this helps I suspect the battery is toast and needs to be replaced. If your friend has AppleCare Protection Plan I suggest that she should contact Apple and see if they can't replace it. Although a battery isn't living forever, so they do need to be replaced eventually.
Hope this gets you in some positive direction.