In most of the cases, that Disk Utility message means that the hard drive is damaged.
However, you can try to erase the disk and restore the Time Machine backup to see if it works. Follow these steps:
1. Insert the Snow Leopard DVD and press the C key while your Mac is starting.
2. Go to Utilities menu > Disk Utility, select Macintosh HD on the sidebar, go to Erase tab and erase the disk. If there's an error during this step, take the Mac to an Apple Store to get a new hard drive.
3. Close Disk Utility, go to Utilities menu, choose the option to restore a Time Machine backup and follow the steps.
If the computer is slow after doing this, take the Mac to an Apple Store as soon as you can
Thanks. I did this, and it worked for a few days, but the next time I restarted it the hard drive crashed again. So, I started over, but with less than 24 hours left the power blinked and the computer shut down. If I restart the reinstall will it pick up from where it left off or start all over (it takes 4 days)?