"Mark246" writes:

Thanks very much, Todd, for the FAST reply, but...
I've already verified that the water supply up to the solenoids is
good.
What other ideas?

Water supply beyond the solenoids of course, or the solenoids
themselves. If they were failure prone, the water one may have
failed before the ice one and would explain your order of failures.

Does your fridge have a filter? Is it beyond the solenoids?

--
Todd H.
http://www.toddh.net/