Your drive is a ST31000340AS with SD15, and now it have a AD14, right?
Congrats, Gradius2! I found the update on the Seagate website, burned it at slowest speed possible, booted the PC and attached the drive after the POST.
The Firmware SD1A-Disc boots up, and if I let it try to detect the drive, the computer hangs and messages like "invalid opcode" appear on the screen,
so it seems that I'm not able to flash my drive with the new firmware.
When I try to flash, I unplug every drive (because the BIOS hangs after recognizing the faulty ST31000340AS - is this the BSY-error?) and restart the computer to re-plug the ST31000 just after the POST. Strange thing: The AD14-Update-Boot-CD (which was recommended by a Seagate employee) does recognize the drive and is able to flash it again with AD14, which is not what I want. So I'm waiting again on Seagate to fix the fixed firmware. ;-)
Thanks for reading.