Hum in a video system usually originates from the video signal ground, especially cableTV. Cable ground is shared through the neighborhood with lots of temporary connections, corrosion, old equipment, etc. That's why it must be earthed again at your house. Check that your cableTV cable is connected to the copper earthing rod as it enters your house. If that's OK try disconnecting the cableTV wire from the system. If that stops the hum even when projector power cord is grounded, then use this on your cableTV input:
http://www.jensen-transformers.com/datashts/vrd1ff.pdfIt is expensive compared to cheap Chinese brands, but they will break over time and this one will last. It is actually a capacitor, not a transformer.
Since the projector is a high current appliance, I would want to keep a safety earth on it and find another way to kill the loop.
You are correct to suspect electrical earth if the projector only has two wires connected, signal and power. If the cableTV idea doesn't affect a change then check the house wiring connections for all of the outlets on the circuits powering the receiver and the projector. You are looking for a loose ground or neutral on any of the outlets on those circuits. Also double check that the bonding cable from the service panel to the earth rod is good. Shut off those circuits before opening up the outlets.
The outlets should have the wires wrapped around the side screws, not wires stabbed into the back holes of the outlet. Tighten all the screws on every outlet of every circuit in your AV system. If you find some are loose, put it on your honeydoo list to check the whole house eventually.
That oughtta keep you busy for a while...
Good luck. You have to have a can-do attitude for ground loops, they can be frustrating. But they can always be solved.