Reinstallazione OS X

elettro Said:

"Reinstallazione OS X: [...]immediately after this, it asks me the Apple ID; I insert my credentials, but the systems says that ID or password is wrong. But they are certainly valid ( although different w. r. those of the previous owner of the iMac, of course ).[...]"

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This may be Locked to a User Account:

Is this a Used Device? If so, the original user would need to enter their information. If you created this with a previous Apple ID, then you'd have to log in with that. This is the link that the seller should have used prior to selling it to you (or whatever is the case): What to do Before you Sell, Give Away, or Trade in your Mac - Apple Support

elettro Said:

"Reinstallazione OS X: Yes, this is an used device substituted by a new model by the previous owner. There is no possibility for me to " reset " the previous users' s credentials and re - install the whole system? If not, the Mac would be unusable, since the previous user did not provide any info."

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Seems you were Scammed:

The previous user should have used the link I provided. They should have known better. They'd have to enter this info --having it sent to their account. Then, once set up --they'd perform as instructed in the link: What to do Before you Sell, Give Away, or Trade in your Mac - Apple Support

elettro Said:

"Reinstallazione OS X: [...]immediately after this, it asks me the Apple ID; I insert my credentials, but the systems says that ID or password is wrong. But they are certainly valid ( although different w. r. those of the previous owner of the iMac, of course ).[...]"

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Verifying if you have a Failing Hard Drive:

Boot into Recovery Mode:

1. Hold Down: command + R upon boot.
2. Go in to: Disk Utility
3. Select: the hard drive
4. Click: First Aid