When i click to "check for updates managed by your system administator" i get 80072EFD. When i click "check online for updates from windows update" i get 80072EFE
How can i fix the problem?
If not, tough luck and time to update the OS.
Either newer version of Win or any GNU/Linux distro of your choosing. E.g Lubuntu does well with old/slow hardware (have that on my old laptop).
Microsoft deactivated the update servers for Vista some 2 years ago. The errors you reported are simply confirming that they no longer exist (both are connection errors). Vista is LONG dead. Time to upgrade.