The restore utility fails to find any Mac os backups on my time machine disks, but they are there. Any ideas?

Question

The Time Machine utility seems to be backing up correctly. The backups appear when I open the backup disk, however, when I try to restore a backup, the utility correctly identifies any disks which contain Time Machine backup files, but when that disk is selected, the utility cannot find any actual backup files.
I have reinstalled the operating system, and repaired and rebuilt all the disks. Apple support suspects that I have a hardware a problem, in that the motherboard is incapable of communicating with some devices. It doesn't matter whether the backup files are on an internal disk, or an external USB drive.
It strikes me as a little weird that the utility knows which disk contain backup files, and will display those disk correctly within the utility, but cannot find any actual backup files, once a particular disk is selected within the utility.
The good news is I have three months to go on my AppleCare plan. The bad news is the closest repair facility is 65 miles away.
Any thoughts on this?

Answer 1

Hitachi HDS722020ALA330:
  Capacity:          2 TB (2,000,398,934,016 bytes)
  Model:          Hitachi HDS722020ALA330                
  Revision:          JK0BB37B
  Serial Number:                JK11H1B9K0AE9R
  Native Command Queuing:          Yes
  Queue Depth:          32
  Removable Media:          No
  Detachable Drive:          No
  BSD Name:          disk0
  Rotational Rate:          7200
  Medium Type:          Rotational
  Bay Name:          Bay 1
  Partition Map Type:          GPT (GUID Partition Table)
  S.M.A.R.T. status:          Verified
  Volumes:
EFI:
  Capacity:          209.7 MB (209,715,200 bytes)
  BSD Name:          disk0s1
  Content:          EFI
Macintosh HD:
  Capacity:          2 TB (1,999,404,957,696 bytes)
  Available:          1.24 TB (1,242,122,113,024 bytes)
  Writable:          Yes
  File System:          Journaled HFS+
  BSD Name:          disk0s2
  Mount Point:          /
  Content:          Apple_HFS
  Volume UUID:          B2577A0B-FA2F-32CE-B8C5-70B9F0C6EB21
Recovery HD:
  Capacity:          650 MB (650,002,432 bytes)
  BSD Name:          disk0s3
  Content:          Apple_Boot
  Volume UUID:          02A41955-B1E4-320A-8FB6-D01019433BEB
ST2000DL003-9VT166:
  Capacity:          2 TB (2,000,398,934,016 bytes)
  Model:          ST2000DL003-9VT166                     
  Revision:          CC3C   
  Serial Number:                      5YD7LBYV
  Native Command Queuing:          Yes
  Queue Depth:          32
  Removable Media:          No
  Detachable Drive:          No
  BSD Name:          disk3
  Rotational Rate:          5900
  Medium Type:          Rotational
  Bay Name:          Bay 2
  Partition Map Type:          GPT (GUID Partition Table)
  S.M.A.R.T. status:          Verified
  Volumes:
EFI:
  Capacity:          209.7 MB (209,715,200 bytes)
  BSD Name:          disk3s1
  Content:          EFI
Alternative Boot:
  Capacity:          2 TB (2,000,054,960,128 bytes)
  Available:          1.26 TB (1,262,551,388,160 bytes)
  Writable:          Yes
  File System:          Journaled HFS+
  BSD Name:          disk3s2
  Mount Point:          /Volumes/Alternative Boot
  Content:          Apple_HFS
  Volume UUID:          7295CED3-FC3E-3DCC-BACF-414390B5DBFC
ST31000528AS:
  Capacity:          1 TB (1,000,204,886,016 bytes)
  Model:          ST31000528AS                           
  Revision:          CC38   
  Serial Number:                      9VP3A6X2
  Native Command Queuing:          Yes
  Queue Depth:          32
  Removable Media:          No
  Detachable Drive:          No
  BSD Name:          disk1
  Rotational Rate:          7200
  Medium Type:          Rotational
  Bay Name:          Bay 3
  Partition Map Type:          GPT (GUID Partition Table)
  S.M.A.R.T. status:          Verified
  Volumes:
EFI:
  Capacity:          209.7 MB (209,715,200 bytes)
  BSD Name:          disk1s1
  Content:          EFI
Internal Storage:
  Capacity:          999.86 GB (999,860,912,128 bytes)
  Available:          999.19 GB (999,194,480,640 bytes)
  Writable:          Yes
  File System:          Journaled HFS+
  BSD Name:          disk1s2
  Mount Point:          /Volumes/Internal Storage
  Content:          Apple_HFS
  Volume UUID:          3074E4E5-9A3A-3C5E-81A9-473C36586C7C
ST32000542AS:
  Capacity:          2 TB (2,000,398,934,016 bytes)
  Model:          ST32000542AS                           
  Revision:          CC95   
  Serial Number:                      5XW29K61
  Native Command Queuing:          Yes
  Queue Depth:          32
  Removable Media:          No
  Detachable Drive:          No
  BSD Name:          disk2
  Rotational Rate:          5900
  Medium Type:          Rotational
  Bay Name:          Bay 4
  Partition Map Type:          GPT (GUID Partition Table)
  S.M.A.R.T. status:          Verified
  Volumes:
EFI:
  Capacity:          209.7 MB (209,715,200 bytes)
  BSD Name:          disk2s1
  Content:          EFI
Time Machine:
  Capacity:          2 TB (2,000,054,960,128 bytes)
  Available:          1.3 TB (1,302,342,303,744 bytes)
  Writable:          Yes
  File System:          Journaled HFS+
  BSD Name:          disk2s2
  Mount Point:          /Volumes/Time Machine
  Content:          Apple_HFS
  Volume UUID:          BC10CF45-B06F-3044-A51E-CBB6A85934BB
And I suspect all of the internal drives are WD, except the start up drive. BUT I also have the same issue if I use a Seagate External drive as my backup location.
What brand of HD would you recommend?