earthlink emails not being sent on my iMac but laptop and iPad working fine. Earthlink tried for over an hour and said to contact Apple.

Ok, then that is telling us that the way Earthlink email account on your iMac may be misconfigured.

I suggest that you remove the Earthlink account from within the Apple Mail app on your iMac. You will be adding it back in, in a moment.

First I would like for you to review both of these support articles:

• Mail - Official Apple Support - Enter your Earthlink email address in the space provided in this article. It should result with the correct email server configurations for your account to use in the Mail app.
• Then use this article on the steps to add the account to the Mail app: Add email accounts in Mail on Mac - Apple Support. Note that you will need to use the "Other Mail Account" option to add your Earthlink account.

Please post back your results.

By "offline" that would indicate that your Mac is having trouble accessing your Earthlink email servers, or there is an issue with these servers themselves. However, since your other devices are not having this issue, it may come down to a configuration setting on your iMac.

As a test, can you access your Earthlink email by using a web browser on your Mac?

Are you accessing your Earthlink emails via the Apple Mail app or via a web browser on your iMac? Was this working before? What have you tried, so far yourself, to resolve this, other than just contacting Earthlink support, so that we don't try offering potential solutions that may not have already worked for you?