I bought it half a year ago. No problem.

I hardly turn off the computer. But I had to do that for 10 hours. Everything's fine.
But when I was forced to ask for a C test drive
with bad sector recovery and reboot for this, then at the verification stage the process failed 14 percent and after my manual reboot the hardware refused to work - yes , a line of text on the screen like: "... or insert other media. ...".

I booted from DVD-Live and tried to run ScanDisk from there, but the computer crashed and after 2 minutes of pause I got a message that a RAW disc was detected and the program was unable to verify it.

I reinstalled Windows 7 Ultimate 64 operating system on new hard drive and tried to connect the broken Seagate-500 Gb to it. it appears in the device manager, but the system immediately asks for its format; I declined and then it disappeared from device manager permanently.

And if I physically disconnect and reconnect (see above), the same story will repeat itself.

What do I have to do now?

Your drive more than likely has physical problems and letting windows run scandisk has probably damaged to the logical side too. What are outcome are you looking for ? If you want to contact a professional service now is the time to do it, recovery will not get any cheaper and this should be entry level.

If you want to try DIY data recovery, it's best to clone the drive before you do any more damage. You can do this with hddsuperclone from a live-cd, you'll also need another hard drive 500GB or more as the destination. Once you have your clone you can use something like DMDE or r-studio to see if scandisk has left any of the filesystem intact. If you're trying to save the drive, don't bother it's not worth it just get another from ebay.

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Data Recovery Services in the UK.
https://www.usbrecovery.co.uk/