My iMac refuses to log me in
One thing to do would be to trick the iMac into thinking its a new setup but jumping into single user mode and deleting the .AppleSetupDone file in /var/db. 

Restart the mac and it'll act like the machine has just been pulled out of its box. (all your data and accounts are still on there). 

Create a new admin account and see if you can login. You should be able to. If not something is seriously broken. If you can, run the standard system checks to see if anything is amiss.