iMac shutting down for no reason

Shuts down at any time and I have to unplug it to get it going

That's an indication of a bad power supply.  Had the same problem occur with a 27" iMac. Had to unplug the power cord before it would reboot.  It was under warranty but took 3 trips to the Genius Bar and several sessions with Apple engineers via phone before it got fixed.  

They wanted to make sure the problem wasn't  software related and finally had me erase the drive and reinstall the system without migrating any of my data over from Time Machine.  When it kept crashing with a new, pristine system they went ahead and replaced the power supply 

If your Mac is in warranty make sure it has a current backup (a clone to an external HD is very good for this type of restore), make an appointment with the nearest Genius Bar and have them test it and, if necessary, erase the HD and install a new, pristine system.  Might save you a couple of trips.  

If it's not in warranty but not considered Vintage or Obsolete (Vintage and obsolete products - Apple Support)  I'd make an appointment to have the power supply replaced right off the bat.  Of course have them run their tests but give them authorization to replace the power supply. 

If it is considered Vintage or Obsolete you'll need to take it into an Apple Authorized Service Provider and hope they have parts for it.

Reset the SMC as per > How to reset the System Management Controller (SMC) on your Mac - Apple Support

If that does not help, make an appointment at your local Apple Store or Apple Authorized Service Provider.

We can also look for obvious problems. Please do the following:

Please post an EtreCheck report of your system and we can look for any obvious issues. Please click the link, watch the slideshow to learn how to use the tool and download and run the free version of the app and then post the complete report it produces as your reply to this message. 

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Well, I think the mystery is solved, at least I'm hoping. You have made a mess of your Mac by adding third party antivirus and MacKeeper which is considered about the worst thing you can do to any Mac. Mac OS is EXTREMELY secure and does not benefit from or receive help in ANY way by having third party antivirus and other third party "maintenance" apps installed. If simply left alone and kept up-to-date your Mac should run well for years.

In your case, you have likely damaged Mac OS. My recommendation is that you do an erase and install and then ONLY restore the data files you need and manually install any third party apps you use. NEVER EVER install any antivirus, cleaning or any other type of third party maintenance app.

In addition, your Mac is starving for RAM, upgrade the RAM to 16 or even better 24 GB of RAM. If you choose to do this only use Crucial.com or macsales.com RAM. Why, simple...iMacs are extremely sensitive to using quality RAM and both vendors supply very high quality products at reasonable prices with excellent service. In short, there is no reason to not use them.

Good luck.