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!