IMac 27″ mid 2011 black screen

I've ran into this issue a couple of times now, this is what has resolved the issue each time. Step 5 sometimes returns a "file not found" error and step 6 doesn't always seem to be necessary but has been in some cases. Regardless, having in their doesn't seem to have an negative effects.

1. Boot to single user mode (hold ⌘ S while powering on the Mac)
2. Type and hit return: /sbin/fsck -fy
3. Type and hit return: /sbin/mount -uw /
4. Type and hit return: rm /Library/Preferences/com.apple.loginwindow.plist
5. Type and hit return: rm /Library/Preferences/loginwindow.plist
6. Type and hit return: rm /private/var/db/.AppleUpgrade
7. Type and hit return: reboot

Assuming all instructions were followed the Mac should reboot and reach the login screen with no trouble. The instructions above should be followed VERY carefully, with attention paid to spelling and spacing, as there aren't many safeguards in single user mode to prevent you from deleting otherwise necessary files.

If you have access to another Mac and a Firewire/Thunderbolt cable you could boot this Mac in Target Disk Mode ( T while powering on) and connect it to the spare Mac to remove the files from the GUI. You would need to open the iMac's system volume (default is Macintosh HD) and remove or rename the two files mentioned above in Library/Preferences.

Hopefully that helps!

Was the mac shipped with 3gb ram? It is possibly not the reason but advice all the same, apple strongly recommends you run ram in identical pairs or individual modules, so a single 1, 2, 4 etc GB stick or 2 x 1, 2 x 2GB and so on, but not 1 x 1gb and 1 x 2gb.