This is at your work? Do you have administrator rights on that computer? If not, perhaps the IT department shut down the service for security reasons. If you DO have admin rights, you can go to Control Panel>Administrative Tools>Services to see if the Windows Update Service is disabled or turned off.
Delayed start just means it doesn't start as soon as Windows boots up. It waits a minute or two before starting. And yours says "Starting", not "Started". How long was the computer running when you got that pic? It looks like the service is having trouble of some sort.
I found this link that might have some useful things to try. Since it is SUPPOSED to be starting, and at least TRYING to start, I approach the limit of what I can diagnose. Sorry I can't be more helpful