Originally Posted by FrysAssociate
OS X recovery disk assistant requires a working os
Thats why I said to install to a thumb drive or boot from another Mac.
Restarted unexpectedly might mean RAM. Have any to swap out? If not, you could run memtest for awhile and see if it catches anything. Otherwise, you could just use the warranty. Unfortunately, there is not much to test in these iMacs that you could test hardware wise.