I checked all of the specifications, there is no reason why the PS3 should not work.
Try this, with everything connected, with the PlayStation 3 off, (standby red) press and hold the power button until you hear 3 beeps, this will reset the A/V settings back to default. The projector should show the PS3 now. Please let me know if you still are having issues.
Hello. My name isXXXXX asked me to be a "second set of eyes" on this problem because it's so unusual. Everything that Jeff has told you so far is sound advice, so this is a little bit of a mystery.
We may have been lucky in that Jeff asked me for my opinion - because (even though some techs - not here - will tell me I'm nuts when I say this) I have personally had several instances where PS3>HDMI>Display simply wouldn't work for me. Even though I could plug an XBOX 360 into the same exact cable, that PS3 wouldn't work with it. I've also learned what might be a little more obvious - that the PS3 signal won't survive an HDMI to Full Bandwidth Digital DVI conversion - even though the signal itself is the same and the only conversion that takes place is the physical connections. I've also had a couple of HDMI switch boxes that the PS3 couldn't communicate through, and I even had a heck of a time getting my PS3 (2 of them, actually) recognized by a 52' SONY TV. My point is, that I'm certain that some cables and junction points along the way, can fail in transmitting a signal that the PS3 will use. So what I recommend is that you try this will a brand new, short, category 2 HDMI cable.
HDMI 1.3 defines two cable categories:
Category 1-certified cables, which have been tested at 74.5 MHz (which would include resolutions such as 720p60 and 1080i60), and
Category 2-certified cables, which have been tested at 340 MHz (which would include resolutions such as 1080p60 and 2160p30).
Despite what some may tell you in a retail store for example, there IS a difference between these certification levels and in my experience the PS3 will not work on a Category 1 cable.
In the 1.4 standard, they are simplified a little bit.
High Speed HDMI Cable
Of course, you want the High Speed HDMI Cable.
My main point is that not every cable will work with a given PS3/display configuration. The cable doesn't even have to be expensive... just get one that's 6ft or less and rated correctly and give it another try.