Your projector powers up, the lamp is ignited and you are able to access the menu and change setting as required. But in spite of all these, one or more of your display ports seems impervious to all effort to get it to work. This could be the VGA, HDMI, S-Video, DVI, and Composite Video ports.
The underlying reason could be either software or hardware. If your projector has internet connection, update the firmware. Remember to always back-up your old firmware before an update.
If no internet connection, you may avail of either the RS-232C port or the USB Type B port to complete the update.
After the update, if the port or ports still would not function, then it is time to either open up the projector and try to re flow the affected controller chip connection pins first, and then the chip itself.
If it still would not work, then you may need to replace the chip outright. This is a component level repair work and you will definitely need the right tool to carry out this repair.
