Q: iMac 27" problem starting

Hi ..

A Safe Mode boot deletes system caches that may help.

Top left corner of your screen click the  Apple   > Shut Down.

After your Mac shuts down, wait 10 seconds, then press the power button.

Immediately after you hear the startup tone, hold down the Shift key. You should press the Shift key as soon as possible after you hear the startup tone, but not before.

Release the Shift key when you see the gray Apple logo and progress indicator.

Once you are in Safe Mode, go back to the Apple  menu. From the drop down menu click:  Restart

About Safe Mode      

Reinstall OS X. Select the relevant choice from the following list.

Install  or Reinstall OS X on Your Mac

1. Follow the instructions in this article for Lion through Yosemite: How to install or reinstall OS X on your Mac.
2. Follow the instructions in this article to upgrade to El Capitan: Upgrade to OS X El Capitan.
3. How to perform a clean install of El Capitan: How to Perform a Clean Install of OS X El Capitan on Your Mac.

You can also try:

Resetting your Mac's PRAM and NVRAM

Intel-based Macs: Resetting the System Management Controller (SMC)