At Walgreen's Drug Store I found something called "Plastic Surgery",
distributed by Superhold, Chicago, IL.  If you can't find it retail,
they sell it on their web site: http://www.surehold.com/adhesives.htm
This stuff is a lot like Superglue except, unlike Superglue, it really
works on plastics.

I had a small but very important plastic piece break off my laptop
computer.  Normal Superglue would never work all that well on plastics,
and although epoxy works a bit better it is messy and hard to work with
for small parts.  This "Plastic Surgery" worked like a charm.  Now, six
months later, that plastic piece on my laptop is still in place and
acts like it never broke off.  Amazing stuff!

Obviously you should test it first if working with "vintage" plastics,
before committing to full usage.  Chemistry can do weird stuff sometimes.

Regards,

Ray Finch
Albuquerque, NM, USA