iMac 2013 27" turns off.

Well you have made a pretty good mess of your system. You have 3 antivirus apps installed when normally zero are necessary. You have:

1. CleanMyMac
2. MacKeeper
3. MalwareBytes

Please uninstall 1 & 2 and if the computer begins running okay you can keep MalwareBytes. The first two are considered malware and can damage Mac OS. Mac OS is EXTREMELY secure and does not require nor does it benefit from any antivirus, cleaning or any other type of third party "maintenance" apps.

Please navigate to the Mac App Store or navigate to www.Etrecheck.com and download the free version of EtreCheck. Once you have you downloaded the app and installed it, please run the report and save it. This report will help us get a good idea what has been installed on your system and help us be able to diagnose what may be wrong.

When you have your report, you can attach it when you reply to this message and we can then review it and help you determine what is needed to get your system running well again. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message please click https://discussions.apple.com/docs/DOC-250000211

Yes, do an erase and install to wipe the system clean and then restore your data files from your backup. DO NOT restore the apps from your backup, only the data files. If that does not solve the problem it's likely a hardware issue.

I also have this problem, it's been driving me mad bonkers! Now apparently it's an issue with the 'power board' and you can get it replaced, I think it costs around £250 to do so, but is cheaper than a whole new motherboard ofc. I haven't replaced mine yet but intend to, as the problem is maddening!