As you can see 5big office is not exactly same as on your 5big. But this person that tried to repair it should have had a reason why to make this scheme. :scratch
The issue is now what device do we have?
About your remark on bios.
Bios is in flash memory or cmos rom. Very unlikely that that is corrupt. More likely is the disk error mentioned by gdisk is the problem and of course if all disks are empty it cannot load firmware.
Now from what I know of lacie devices is that a 5big has been sold in two versions, one diskless and one with disks.
The diskless version contains a nand flash with basic firmware that is loaded to disk when inserting an empty disk. In this case empty means a disk without a partition table. If yours was originally a diskless one you could try this.
T,ake a disk, delete partition table using gdisk (don't forget to use "w" comnand to leave gdisk after deleting partition table to really erase partition table. And put this empty disk in your nas (most left slot) and see if it installs firmware. You should see a blue led on disk 1 after a while flickering with disk activity.