iMac 2012 27" waking from sleep will not start

Lately, my iMac 27" has not properly awakened from sleep mode. When I attempt to enter the password, the computer manufactures its own string of digits in the box and then refuses to open. The only way I can start the computer is to power down from the button on the back and use it to power on. But, after using the computer and either putting it to sleep or if it puts itself to sleep after timing out, I have the same problem. I have tried resetting the SMC and the PRAM, but the problem persists the next time I try to use the computer from sleep mode. Any suggestions? Thanks.

iMac 27" late 2012 using El Capitan 10.11.2