I have sound, but picture is black - Philips 9P5034C 50" Rear Projection Television

This is an old-style tv, one in which the image is produced by 3 small tv tubes and then projected on the screen. Since you have sound it means that the defect is situated in either the video processor and finals or the tubes themselves have either failed due to old age or they aren't powered. To find out which you must open the tv and test it.
Start by removing the back and just look at the tubes: if their necks aren't lit when the tv is on then the tubes aren't powered - you will need to check the contacts on the base of the tubes and reseat all of them (don't forget to pull the plug and wait for 15 minutes before doing that). If the tubes are lit you will need to check the voltages on the electrodes - start with the cathodes. If all the voltages appear to be ok then it's in the video section - find out if the video transistors are powered correctly and operational. If they are then it's the image processor - luckily in this tv it can be replaced , with some effort, individually. You will just need to find and absolute exact replacement.
All of this requires a good electronics experience. If you don't have it then it's time to call a pro.