I found that there is an 'information' in the system event log: "\SystemRoot\System32\igxpdx32.DLL failed to load". Microsoft had no information on that. Well, i'd say that's an error. I googled on that error message, and fond an answer.
That person, Argorian, obviously knows more than Intel and Micorsoft together...
Anyway, the solution is to increase the session image size to 0x20. It is in the registry, so just run regedit andfind: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Session Manager\Memory Management\SessionImageSize. On my computer it was 0x10, so I changed it to 0x20 as advised, and rebooted. Voila! Both the television set and my secondary monitor sprung to life, even without me changing the display properties! Windows probably remembered my setting without showing it.