Last night I finally gave up on Vista and reverted back to my XP installation, but WMP Media Sharing was still broken — luckily I stumbled on a error message from WMPNetworkSvc in the Event log when I was actually looking for something else:

A new media server was not initialized because WMCreateDeviceRegistration() encountered error ‘0x80070057’. The Windows Media DRM components on your computer might be corrupted. Verify that protected files play correctly in Windows Media Player, and then restart the WMPNetworkSvc service.

For more information, see Help and Support Center at http://go.microsoft.com/fwlink/events.asp.

Unsurprisingly the Help and Support Centre was no help at all, but simply plugging that entire error into Google turned up a lot of people having the exact same problem, and I found the solution to my troubles here: http://www.ureader.com/msg/15751792.aspx

I searched the net for this, and found this: http://forums.techarena.in/showthread.php?t=686560

After checking the registry I found that on my machine the setting pointed
to:

C:\ProgramData\Microsoft\DRM

This folder was there, but maybe one of the files was corrupted? I moved
everything from the folder to a temp folder and then restarted the service,
and Voila! Now everything works again.

-Mikko

Finally I can stream video from the PC to the 360 again.