Here's what I'm trying to connect:

Phillips DVD Recorder Model DVDR3400 (which has 1 HDMI input)
DirecTV HD Receiver (which also has 1 HDMI input)
Panasonic Plasma HDTV Model TH-42PX60U (has 2 HDMI inputs)

And this is what I have in the way of cables:

1 HDMI cable
1 component video cable (the YPrPb cable)
1 S-Video cable
And plenty of composite video cables

How do I connect it all so that I still have a great picture and am able to record programs from the satellite dish?

Best bet is to connect the HD receiver to the Philps using Component video, then the Philips HDMI output to your TV.

From what I've read, The Philips Component video input only accepts 480i, standard definition signals. You may need to set the HD receiver to output 480i in order to record properly.