Quoting Josh Dersch <derschjo at msu.edu>:
Hi all --
Picked up an Apple III this weekend in non-working condition, and I
suspect the power supply is at fault.
Symptoms are: On power up, a rapid clicking noise is emitted from the
power supply (maybe 4Hz or so), and the power LED on the system's
motherboard pulses at the same rate. Obviously I haven't run it for
more than a few seconds like this :).
--Snip---
Last time I had a power-supply that was clicking there was a bad transistor and
a couple of failed caps...