Bought iMac second hand locked

The purpose of firmware locks and other passwords is to dissuade theft of property and data.

Apple will require that you provide the original retail sales receipt before they will provide access to a locked iMac or device.

An other receipt (eBay, Craig's List, etc.) is unlikely firm evidence that this iMac was not stolen.

At Apple, privacy is Job 1... just ask the FBI. 😉

If you know the seller, you should approach them to unlock this iMac, or provide you a copy of the original sale receipt.

What the seller should have done prior to selling the iMac to you:

What to do before you sell, give away or trade in your Mac - Apple Support

+1 return the thing, If you don't want an Apple Refurbished Mac (they're great and what I'd buy) then buy a used Mac from a reputable source such as Macsales.com. NEVER buy from Ebay, Craigslist, MarketPlace or anywhere that you do not personally know and trust. As stated a used Mac from a private owner should be setup per What to do before you sell, give away or trade in your Mac - Apple Support If it was not then you got the short end of the deal and have to deal with a mess which you are quickly learning. This is not an Apple issue at all, it is an issue created by a seller and uneducated buyer. Sorry to sound harsh however it's correct.

Really though, best of luck and please return the thing ASAP!

I believe the bottom line here is only IF you have the original sales receipt (which should include the serial number) for this second hand iMac, then Apple may be able to assist you with this. I recommend you make an appointment and carry the Mac to an Apple Store or Authorized Apple Service Provider for service.

Start here for that option:

Genius Bar Reservation and Apple Support Options - Apple

If the iMac was improperly prepared for transfer to you then that is on the previous owner and you should request a refund.

If you bricked the iMac with a firmware password then that's on you.

If you still have access to the machine after it restarts, then a firmware password is not the problem.

If you need to reset your login password, this might be helpful:

If you forgot you Mac login password - Apple Support

Your comments about an iPad and MacBook Pro are irrelevant to the iMac problem, but if you are having problems with those, then you should start new threads about them so the issues might be resolved.

Good luck, my friend.

Were it not for the firmware password, there would be workarounds. In this case, frankly I'd demand my money back and look at Apple refurbs for a good price on a computer with a full warranty.

Refurbished Mac - iMac - Apple

What exactly did Apple tell you? Was this at a store, online or phone?

AppleCare is not relevant to unlocking a locked Mac. You're going to have to provide proof of ownership and proof that you are the person listed on the sales receipt. Did you buy from a legitimate reseller or from a friend?

In the admittedly few cases I know of, it was done in person at a store.