I'm glad to say that I found the problem. I replaced the RFX6000 with an RFX6500 and the problem disappeared. Windows Media Center worked perfectly. Also, every single component, there is much less of a delay between pushing the button and the command being accepted by the A/V system.

I knew the RFX6000 was less-reliable as far as interference, but I didn't know that some codes won't pass correctly at all and I didn't know how much slower it was. I was going to use the RFX6000 in a second room, but now I'm thinking of using it as a target for a hammer. At least Philips did redeem themselves and release an improved version, but they need to apologize to everyone who purchased the first version.