Won't boot into safe mode
My 2012 iMac 27" was randomly rebooting itself, while in Sleep. I assumed this was due to the cheap 32 GB memory I bought, but before I could change it back to the original memory, to test, the Mac booted into Safe Mode (I assume - a progress bar showing at the bottom of the boot screen, below the Apple logo), and did not get further than a half the way, and then shut down. I swapped the memory to the original 8GB. I tried booting again, no buttons held down, as then it wouldn't get further than a quarter of the way. Further attempts to boot do not work, even when holding down Option to choose the boot disk, pressing Shift for Safe Mode, or Option-S for Single User Mode. I assume it's trying to boot in Safe Mode, but failing?
I also tried using a good Mac with the bad Mac as the Target Disk boot mode - the good Mac does not see the bad Mac...
I have an external DVD drive, but that isn't an option as I can't go into boot drive select mode. What are my options, apart from sending the iMac back?
iMac, OS X Mountain Lion (10.8.2), 2012 iMac 27" 3.2GHz i5