I had some trouble with the display: some segments didn't light up reliably. Turns out that one of the common cathodes had a loose connection -- nothing a drop of solder didn't fix.
I also had trouble with initialising the communication between the PC and the PIC (via serial port, of course). I programmed a small fix for that today, and it all works reliably now.
And... I soldered the serial infrared receiver circuit and hooked it up to the remaining COM port. I have had the parts lying around for a long time now (I'm guessing about a year), and I never had gotten around to construct it. Upto now, I have used the receiver of the Winamp Remote Control and I used the RealMagic Remote that I bought to go with the Hollywood Plus I used prior to the birth of the MACH F to play DVDs.
There was still some space left on the display-board onto which I could fit an IR-receiver IC. And I also had some space on the print free for the ridiculously simple circuit -- so, while the soldering iron was still hot, I added it to the display.
And it works! I reconfigured WinLIRC to use the 'internal' COM-port, and it all works like a charm. Even through the plexiglass of the drive bay, the remote control is responsive. And it seems like I have an ever larger receiving angle than with the external receiver.
Needless to say, I am pleased.
If anyone is interested in having their own remote control receiver for use with, for instance, WinAmp or BSPlayer, talk to me. The parts cost only about 4 euros or so!