Computer turns off instead of going to sleep mode. Have to unplug from the wall to get it started again

Howdy Lana_Shch,

If you are having an issue with your iMac shutting down when you try to put it to sleep or when it goes to sleep through inactivity, I would suggest the next step would be to reset the iMac's System Management Controller. See this article for directions -

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

Specifically -

Resetting the SMC for Mac Pro, Intel-based iMac, Intel-based Mac mini, or Intel-based Xserve

1. Shut down the computer.
2. Unplug the computer's power cord.
3. Wait fifteen seconds.
4. Attach the computer's power cord.
5. Wait five seconds, then press the power button to turn on the computer.

Thanks for using Apple Support Communities.

Best,

Brett L