Some older games simply were only designed for interlaced display, and not progressive such as with 480p. The Wii makes this mode for Virtual Console games available via the component cables. The result can however be that the games start successfully, and you can here the sounds, but the screen goes completely blank.
How do you fix this? Easy.
Take a look at this extract from the Wikipedia Virtual Console article which tells you how to get around the issue.
Initially, some PAL Virtual Console games would not display correctly on high-definition televisions when connected via the component lead. However, starting with the April 13, 2007 update of the PAL Virtual Console, certain newly added games, such as Punch-Out!!, support the “Wii Component Cable Interlace mode.”
This is a temporary fix to problems with various Virtual Console games being played over component cable on HDTVs. The mode can be enabled by accessing the operations guide of the game, and (with the Nunchuk attached) pressing the buttons Z + A + 2 simultaneously. A sound is played if the mode is enabled correctly.
Several older games also have updates available to enable the feature, such as Super Castlevania IV. The mode can be disabled by using the same method, but with the button combination Z + A + 1 instead. A full list of games supporting this mode is available at vc-forums.com.