Exact error:
System error 1075 has occurred.
The dependency service does not exist or has been marked for deletion.

Symptom:
Viewing any Windows XP/Vista service “Dependencies” tab in Control Panel > Administrative Tools > Services, throw an error.

Possibly cause(s):
Broken Windows Management Instrumentation repository.

Purpose:
Windows Management Instrumentation (WMI) is the infrastructure for management data and operations on Windows-based operating systems. You can write WMI scripts or applications to automate administrative tasks on remote computers but WMI also supplies management data to other parts of the operating system and products, for example System Center Operations Manager, formerly Microsoft Operations Manager (MOM), or Windows Remote Management (WinRM). Taken from here.

More reading regarding Windows Management Instrument here.

Fix:
Note: all of the commands below executed from Windows command line.
[*] Stop WMI service:
net stop winmgmt

[*] We will rebuild the repository, rename the folder to something else as a backup.
ren %windir%\System32\Wbem\Repository Repository_old

[*] Start WMI service:
net start winmgmt

[*] Repair the repository:
[*] Windows XP:
rundll32 wbemupgd, UpgradeRepository
[*]Windows Vista:
winmgmt /salvagerepository

[*] Register the new WMI components:
cd /d %windir%\system32\wbem
for %i in (*.dll) do RegSvr32 -s %i
for %i in (*.exe) do %i /RegServer


[*] Reboot the computer for the changes to take effect.

That should fixed your WMI repository.

If all above steps doesn’t work for you, try comprehensive rebuild below:
rundll32.exe setupapi,InstallHinfSection WBEM 132 %windir%\inf\wbemoc.inf

Above command will ask for your Windows XP/Vista installation disc.

Update #1:
——
One of my reader which having the same exact error message as stated above, but different problem. His problem was the Windows Firewall service on his computer cannot be started, stopped, nor restarted. Suggested to reset the winsock instead. Launch command line and execute the following command:
netsh winsock reset

This method works for him, I just put it here for your reference — in case you have the same problem.
——

Update #2 – Jan 28, 2011:
——
The same issue but on Win2K SP4 and solved with the following command:
rundll32.exe setupapi.dll,InstallHinfSection InstallService 132 %windir%\inf\wbemnt5.inf
——

Please let me know if this how to doesn’t work for you.
Good luck.

Windows manual book for troubleshooting reference: Windows 7: The Missing Manual