It's to do with the way the display is manufactured - it will be some kind of LCD screen that uses polarizing filters in its construction (google: 'how lcd works' and 'how polarizing filters work'). Since the light leving the display is already polarized (travelling in one direction), when it hits your sunglasses it is blocked because they must be polarized in the other direction. That's the reason why turning your glasses 90 degrees alows the light back through, as the polarization is now in the same direction as the display! I would have thought most lcd screens would suffer to some degree, but it depends how good the display and your sunglasses are.
Try putting various bits of plastic sheeting in front of the trip computer (I suggest you try clear plastic bags, cellophane, the wrappers from cigarette packets etc.. Also thicker plastic like CD casing might work).
The problem is that the LCD on the trip computer has a polariser in front of it (just part of how LCDs operate), which is apparently oriented to produce horizontally polarised light - exactly what your polarising sunglasses remove! Various polymer films (i.e. plastic sheeting) are birefringent, which means that they can change the polarisation of the light. If you find just the right type and thickness, it should let you see the trip computer again!
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