When you stated you tested the cable. Did you do so by trying different sources with HDMI outputs feeding the projector, or with an HDMI Tester or pin to pin continuity test ?
Also, when you state "decent quality" cable, who is the manufacturer?
HDMI cables were originally designed to run up to lengths of around 10 feet. Many manufacturers promote that through better construction and larger conductors, their cables can far exceed that. With most of the major manufacturers, I would have some faith in their claims. With many of the generic cables out there as seen on many ebay auctions, I would have my doubts, though the promote their cables as Premium Quality.
"if you can't find the answer to life, change your questions"