iMac frozen on login screen

Not much information. I assume you have ElCapitan.

First do the "Pram reset":

How to Reset NVRAM on your Mac - Apple Support

Try again.

When it still freezes:

Press the ON button to start and then press and hold the Shift key, it should start in the "SafeMode", it is slow, when you see the login window, login. After login, open Finder.

Does that work? If yes, restart normally.

If not: Restart while holding the CMD+R keys: it starts, slowly, in the "RecoveryPartition", choose DiskUtility form the menu, in ElCapitan click the FirstAid button, let it do its job, any messages?

in older OSX choose DiskUtility and do "repair permissions" and "repair disk".

Restart.

Could you enter the Recovery Partition at all?

Do you have a TimeMachine backup?

If yes go back into the RecoveryPartition, then from the main menu choose "restore from TimeMachine".

If that does not work, I suppose it is a really serious problem either the disk or something on the main board; and then a visit to the Apple Service is necessary: there is a so called Apple Hardware Test (AHT) for users, but is is rubbish: if it finds a fault, it says so, if it says all OK there still can be a hardware fault. Apple service have a very good and reliable hardware test.

keep us informed... we want to learn too.

Lex