2017 iMac difficulty starting with power button

Reset the SMC, as per > How to reset the SMC of your Mac - Apple Support

Desktop computers

1. Shut down your Mac, then unplug the power cord.
2. Wait 15 seconds, then plug the power cord back in.
3. Wait 5 seconds, then press the power button to turn on your Mac.

If that doesn't help > contact Apple Support and setup a service appointment.

After you're able to reboot your iMac does it shut down by itself after some time?

Did den.thed's suggestion work in letting you immediately reboot the next time you pressed the Power button?

If the next time you shut down manually and you can't reboot easily it may be an indication of a failing power supple. Unplugging the power cable briefly to let it reboot is a sure sign.

Make sure you can a full and current backup of your boot drive.