Hi Hiheyho!
I'm in exactly the same position as you and - sadly - so are several thousand of other Seagate users around the world.
Here's the situation as I see it - but I'm no disc expert.....
3 days ago my Seagate 1Tb Barracuda was working absolutely fine. I powered down for the night and following day neither of my Seagate Barracudas (1Tb and 750Gb) were recognised by my bios! Let me add that my new tower is less than 3 months old here! I thought along the same lines as you originally - that it might be a cable problem since I'd done absolutely nothing to change any of my bios settings - but I frigged and sodded about with different SATA holes, changed cables etc... none of which solved any of the problems so I switched off and left it for a few hours. When I had another crack at it that afternoon, the 750Gb disc with the OS on it came alive but the 1Tb one is still dead. I did some Internet research and found - literally - thousands upon thousands of cases where Seagate Barracudas just 'die' for no apparent reason at all. The fault always seems to be with the onboard firmware that just gets corrupted and - whilst the electronics may still be functional - it no longer looks like a disc drive to the bios.
Now! There's 1 ray of hope here.... I rang Overclockers today and arranged an RMA (which they gave me) but meanwhile, I - like you - need to get to my precious data to back it up. The techie suggested mounting the drive in a USB 'caddy' as this negates the need for the bios to recognise the actual disc itself since the caddy does the ident at boot time.
It means, of course, that your OS has to be able to support an external USB drive but this MAY (and I stress MAY) just work. For your info, I've been looking at the following caddy from a company called USB Now.co.uk and it looks like being the chaepest option in case the work-around doesn't!
http://www.usbnow.co.uk/External_Hard_Drives_&_Cases-3.5%22_Hard_Drive_Cases/c10_25/p1365/Probox_SATA_HDD_to_USB_2.0_Interface/product_info.html
Take a look at this one and see what you think. Like I said, I'm no expert but we are not alone with this problem. I just hope someone from Seagate takes a look at the number of people afflicted by the same problem and bangs a desk somewhere 'cos it seems to be a 'known problem' for which there is no local repair and if you can't back up your data you just have to grin and bear it! Wish you luck mate! I'm waiting for a response from USB Now to see if they agree with my proposed solution....
Cheers and merry christmas!