Spinning Wheel after

I have a Macbook A1181 Mid2006 ver 10.6.

All worked fine on my daughter's macbook / up to installing from a few apps from Itunes / kids math apps.

I did the install using the admin account; I then did a restart after the app installs and anticipated logging in with my daughter's username.

The boot screen began with the Apple in a grey background, then went into a light blue screen with the spinning circle coming and going as it spins. I held down the shut down button. Unplugged the machine, removed the battery, replace the battery, plugged in the power cable -but I keep getting this spinning wheel routine.

I did restart holding the Shift key/ and I could see the bar moving as the machine attempted to boot into safe mode, and again, the system went to blue screen with a spinning wheel.

I then did a restart with with Command + S; ran fsck -fy - and got a 'the volume appears to be OK' ; did a reboot, passed the Apply logo into spinning wheel on blue.

Let me know what to do. It is my daugher's Macbook - I have no expertise in Mac/Apple.
Thanks!

Use the Snow Leopard DVD and boot from that and run Repair Disk in Utilities. To boot from the DVD, pop it in, restart, and hold down 'C' after the chime. With the age of the machine first suspect is a failing hard drive.