I have one of these (it was my first computer too, as in the first one that I owned) and stuck a couple of batteries in it some months ago. It immediately booted up, I was quite surprised that it had survived 3+ decades in storage without any trouble at all. The weak point in old hardware is capacitors and my guess is that because it is battery powered and has no need for much power stabilization that all the caps in there are either small or non-electrolytic. Props to Sharp for building an extremely rugged product, I don't have any other hardware from that age but everything I bought after that has died by now.
This may come in handy:
http://www.scribd.com/doc/48707750/sharp-pc-1401-manual