startup issue

1. Check the power cord on the back of the iMac, to make sure that it is firmly plugged in.
2. Check the outlet where you are plugging the iMac in, to make sure that it works.
3. Try plugging the iMac into a different wall outlet or different location.

also see > https://support.apple.com/en-us/HT204267

Then if your Mac still doesn't turn on, please contact Apple Support.

What do you mean by a new location? Attach to a different LAN or ISP? Physically different as in a different room or house?

Please supply full details on your Mac as found in "About This Mac" under the Apple icon at upper screen left. Leave off the serial number.

Also, if you're having other problems, please detail them too.