My HTPC is connected to my 990 via DVI. The computer is up 24/7. However, I occasionally (though rarely, thanks to Linux) need to reboot. When I reboot while the 990 is turned off, my display does not pass through the 990 once I turn it on (similar to what you are experiencing) until I reset the video mode which allows my video card to detect the display.

In your case, and if I understand your post correctly, going VGA to component and back to VGA, that may make it impossible for your video card to recognize the display unless you manually force it to a specific mode and frequency, which may be dangerous to your projector.

Have you experimented with the video mode switching on your PC? Some computers use a hot-key like Alt-F8, Alt-F5 or Ctl-Backspace to reset the video mode or cycle through modes. This will use the detected display's frequencies and should not be dangerous. The risk to your display comes if you want to manually set monitor type and frequencies using trial and error, which I don't recommend and should only be done if you know exactly what settings to use.