Will not boot, erase or reformat

Mac has seen us good for 3+ years. Recently it started to run very hot and then stop working, screen would blank out. A restart would get us going again. Now the machine won't boot past the white screen with grey Apple and spoked wheel spinning.

Have followed Macforums troubleshooting: Safe boot, NPRN reset etc.

Have run Disk Utility from OSX Snow Leopard.

Disk Repair failed: Told to back-up, reformat and restore.

Disk Erase attempted several times with following results: Disk Erase Failed with error

1. File system formatter failed

2. POSIX reports: Cannot allocate memory

3. Assert: internal error or implemented

Attempted to re-install Snow Leopard and message: The contents of this disk can't be changed. MAC OSX couldn't be installed on this disk.

Have noticed that grill on base of Mac was pretty much full of dust. Have I fried the hard disk?

Love the video and manual. Keen to fix this with my 12 year old.