Q: iMac won't go into recovery mode. just goes to grey screen with apple logo and spinning gear then restarts over and over?

Recovery mode is only available to iMacs released new on or after August 8, 2011 as an educational model, or October 23, 2012 as a regular model.

The one exception is if you install a special firmware:

Computers that can be upgraded to use OS X Internet Recovery - Apple Support

To determine if that firmware is installed, you need to go here:

Intel Macs and their firmware

Try booting off an external hard drive or holding the shift key on startup if it won't boot otherwise.  You may need to bring it in for service if you didn't make a bootable backup initially.