My frantic googling today found a few references to a few people who thought that Intel's implementation of HDCP in the HD Graphics chipset may be flawed, or at least finicky when interacting with devices having quirky implementations. This makes sense to me, considering that HDCP is the one "feature" in HDMI whose entire purpose is to cause the entire product to fail if something goes wrong with it.
I might have to just return this monitor and get a new one... I've hooked this laptop up to a couple of different televisions with no problem. If the issue does turn out to be HDCP, I'm definitely making a donation to Defective By Design after this BS.