sounds like you have a few problems going on with the flower power mac:-)
First off Disk Warrior is a great program I use it all the time at work. I would try safe boot first. and then try disk warrior. Safe boot does a few things with the system here is more info on it
http://docs.info.apple.com/article.html?artnum=107392
Secondly it does sound like the battery could be going. however, it could also be becuase the PMU button on the logic board needs to be reset. Doing both those things requires the bottom housing on the mac to be taken off. Something you might want an apple service center tech doing.
Just to Clarify, she starts the computer, the apple appears, the gear below it spins, then the desktop appears and that is where she gets the spinning color wheel?
If that is the case the problem might be in the user account she is using on that mac.
firstly I would let the ball spin for a while to see if the account or OS needs to load or configure something. fonts for example are bad for making that spinning ball spin for sometimes up to 5 minutes ( I know from experience)
However, here is what she can do if the ball spins past 5 minutes.
restart the mac in safe mode (holding the shift key)
when the desktop appears under the blue apple menu select system preferences.
look for the account option. select it and create a new user. she might have to click on the lock icon and enter a password to do so. plus to make the new users u click on the plus + button just above the lock
then try logging in as that user to see if the problem is fixed.
I have set up a few users on my own computer for when I have load problems like you mentioned.
Let me know how everything goes