Video link: https://www.youtube.com/watch?v=EfUWdDy-0Rc

The HD shown in the video is a Seagate Freeagent GoFlex portable, model STAA1000101 (FreePlay 1000GB).

Is this beep a known signal? What does it mean?
Would replacing the PCB, with a BIOS transfer to the new board, possibly fix it? I know it's hard to tell, but if it has any chance of being fixed, I'll do it, since I'm out of options.

Thanks in advance.

The sound you hear is the drive's inability to spin up.
Judging by the picture it is most likely ST1000LM010 model.
These drives sometimes create so-called "heads sticktion", especially if you drop them. Unfortunately they also tend to bend HGAs when they create the sticktion and that complicates the recovery process.
It is not possible to judge drive's conditions without opening it. Please don't open the drive yourself, it is unlikely that you would be able to fix it but it might complicate the recovery further and increase DR price.
Seek professional help if you need data.

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SAN, NAS, RAID, Server, and HDD Data Recovery.

Head stiction video by Waqas Ali:
http://www.mediafire.com/download/cvo59 ... k_head.zip

Waqas Ali is a SalvationData trainer:
http://www.alexsoft.org/viewtopic.php?f=88&t=622&p=1671

Of course he would normally perform the procedure in a cleanroom or clean chamber, and he would be wearing gloves.

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A backup a day keeps DR away.