I need a very accurate linear position sensor, that can measure verticle
object travel of approx 1.5 inches. Cost is an issue. It will be an input for
a PIC16F84, so a digital signal would be less work.

Can anyone help?

Try this....
Mouse ball princable and a fixed sensor to check end of travel......
a slotted (laser etched) strip and a slotted opto switch with an additional
switch opto or mechanical to indicate 'home'
Alternatively if the mirco is controling the movement a single switch to
signify end of travel and a steppermotor driving a worm gear to move the
object sorting out the position is a matter of counting steps.
Alternitivly read the thread on 'reading a pot without a-d and use a pot

Just a couple of ideas....

Cheers Steve............