a solution not using pics
ok this wouldnt be proper randdom, but then again its fairly hard to get 'real' random.
use a very fast A stable, say a 555 clocking at say 1MHz, this is used as the clock pulse for a counter.
with the counter lint the 7th output pin to reset.
use a switch to trigger a 2 second monostable. the monostable when triggerd will stop the 555 astable by holding it high.
the display will be a set of 6 flashing leds, if you get the astable fast enough they'll all look as if there fully on. when you press the button the monostable will stop the the sequence at a praticaly random position. the only problem being when its reseting you wont get any leds lit this will be 1/7 times aprox.
also it will have a relativly high power consuption, but nothing to bad.
its a simple way of doing it, would work better if you could find a counter chip that has a display enable pin, so you can turn the display off while its flashing.