All those who said to look at the power were, of course, right. There's a
programming connector added to these boards that basically consists of a
2X5 pin header with 30 gauge jumper wires running to vias on the board.
In all the handling this board got, the tiny wires had been weakened, and
were on the verge of breaking at the board join. In fact, the moment I
tugged on some of them, they let go. In operation, one par of these
wires, of course, carries Vdd, another pair Vss...

I removed the connector, cleaned up the board, and soldered on a new
connector, and now all seems well: the board starts up immediately and
repeatably, like the other 3.

But I want to make sure this design is solid, so I have another question:
Harold Hallikainen wrote about Murata's search engine of resonators
tested with actual PICs, so I checked it out (bravo for Murata, BTW!).
They don't list any of the PICs I need (16F877 and 16LC774), but I poked
around a bit, and it seems that for *every* instance of a Murata
resonator and a PIC, they specify an external 1M resistor (Rf) across the
resonator leads.

But in the PIC data sheets, that same resistor is shown as built in to
the PIC, and it says the value varies with the crystal used: I assume the
configuration bits are what changes the value.

So the question is, do I add that 1M resistor, or assume the PIC has
handled it? It seems to work just peachy without it, I haven't tried it
with, and suppose I ought to, but what's the safest thing to do here?
Harold, did you add an external Rf?

Dave Johnson