If they can’t guarantee to get the data back off it then you can (probably) do it yourself – it will obviously void any the warranty on the drive though so it’s worth checking first.
The LaCie disks are really just a standard IDE disk in a metal case with a bit of circuitry to connect to the firewire and power the disk. If anything’s fried it’s almost certainly this circuitry and the disks are fine.
So you can take a screwdriver and a deep breath, take the back off the drive (there’s a screw hidden under the ‘Warranty void if removed’ sticker), take the disk drive out and put it into your Mac. Then copy the information off it onto another FW disk, or buy another disk chassis and put it in there.
The only fly in the ointment is that the BigDisk Extremes have two disks in them, configured as a RAID (any LaCie disk that’s twice the length of the old ones is like this). I’ve never done it with one of those – in theory it should work ok but has anyone else had practical experience of it? I think that you should just be able to get hold of another two-disk IDE chassis (G-raid do them) and put the disks in there.
Make sure that you keep them the same way around (one is primary and one is secondary) when you do it though, or get a techie friend to do it for you (then you can blame them if it goes wrong -only joking! :-p)
Good luck!