i MAC desktop

If your iMac does not turn on at all,

see > If your Mac doesn't turn on - Apple Support

Also check the power cable on the back of the iMac and try a different outlet.

If you iMac does not startup all the way,

see > If your Mac doesn't start up all the way - Apple Support

Give the following user tip article a try:

• Mac Basic Startup Troubleshooting Steps - Apple Community

Do you know what year yours is? That may help us, as some sub-models had known issues.

With the computer a non-runner, you can find the serial number under the "foot" of the stand:

and use another device to enter the number into this Apple Support page:

Check Your Service and Support Coverage - Apple Support

That will return the sub-model like this:

In the results, "27-inch, Mid 2010" is the sub-model of the sample.