I have a Seagate Barracuda (ST31000528AS) with the infamous "burnout" issue on the PCB.
I've tracked down a replacement from none other than Mr Eric Lee, but he says on some drives I must solder on the BIOS chip from the old board. That leaves me with 2 questions:

a) Is this one of those drives?
b) Which chip is the BIOS chip?

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Apple Store New Orleans

The fact you need to ask this tells me that you should probably not be working on this case on behalf of a client, and the fact you only know this because you were told by Eric Lee confirms it!

In answer to your question, the 'BIOS is actually the EEPROM and is a 8 leg chip found usually at the top left of the PCB, and yes it will need to be transferred. You should consider the initial problem that caused this damage, and be aware of the possibility that other issues may arise.

There is no Apple Store in New Orleans, and even if there were, it is against Apple's corporate policies for an employee to post to a public forum as such. So why are you posing?

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http://www.datasaversllc.com

But why stop there when you can also use Apple logos and branding without permission and sell iPhone unlocking?

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You don't have to backup all of your files, just the ones you want to keep.

It may be much easier to fix your original board. It looks as if it has a shorted TVS diode on the 12V rail.The fix is to remove it with flush cutters. The drive will work without it, but it will no longer have overvoltage protection on the affected supply. For continued protection, you can replace the diode with a SMBJ12A from Mouser, Digikey, or Newark.

BTW, were you warned before your purchased the board that you would need to swap the PROM?