In your Start menu, right-click "Computer" (or "My Computer" if using XP) and select "Manage".
Expand "Services & Applications".
Open "Services". (Perhaps maximise the screen to better see what's going on.)
Right-click the Bonjour Service and select "Properties".
In the General tab, set the Startup type to "Automatic":
... and click OK.
Restart the PC. Do you still get the message about the service being disabled?
wait .. I am a dolt! I am on the other computer where it works.
It DOES Not work on that computer, In Services, there is no mention of Bonjour! as I said above.
Sorry about the false-start .. it is not working nor installed ... I happened to get the email on this one and click the link. my bad
the screen shot DID come from that computer
I moved a Bonjour folder over from the known good/bonjor Windows-7 machine. Then I executed mdnsresponder.exe -install. On that computer, Bonjour shows running/automatic. Yet iTunes still complains it is not installed. I suppose I have to re-start a thread on this topic as no one will bother to look anymore if it seems solved. me bad
For general advice see Troubleshooting issues with iTunes for Windows updates.
The steps in the second box are a guide to removing everything related to iTunes and then rebuilding it which is often a good starting point unless the symptoms indicate a more specific approach. Review the other boxes and the list of support documents further down page in case one of them applies.
Your library should be unaffected by these steps but there is backup and recovery advice elsewhere in the user tip.
The section Install missing components has advice on breaking down the iTunes installer into the individual .msi files which might prove useful if one component, such as Bonjour, won't install normally.
If needs be, the Microsoft Program Install and Uninstall Utility (MS Installer "Fixit") may be able to help force through the installation.