The one you mentioned with the silicone spray is for the gauge cluster, not the radio display. I would never use silicone spray for electronics anyways... I would recommend simply a contact cleaner. But for the radio display fix it is a ribbon cable that gets funky contacts to the printed board with the display. And unfortunately it is not a connector, but the ribbon cable "clamped" straight to the board. The fix is to trim 1/8" or so of the cable to get to fresh wires and re-fix it to the board. But like I said, it is a short, wide cable with not much slack to work with.
I just searched around and the link wasn't on this site, but on bimmerboard. It shows the repair being done on an E39 display, but its the same for the E53. Here's the link.
http://www.bimmerboard.com/forums/posts/504260