When I turn it on, it opens as it should, but shows "Card Full". Card
is not full, as confirmed by inserting any other one of my four empty
cards.
If turned on with no card in, it shows "No Card", as it should.

I noticed that all of the menu screens that I get to by navigating
through them, show the last settings they were left at before the
failure, except that the date setting has reset to 0000/1/1, and the
time shows 0:00.

Any suggestions what to do? I cannot afford a replacement just now,
and I need a digital almost daily in my work.

Remove the batteries and let it sit for at least 24 hours. This should cause
the camera to completely re-set itself. Once in a while the older Olympus
cameras would freeze up like that; happened a couple of times to my Olympus
450Z (the predecessor to your 460).

--Mike-- Chain Reaction Bicycles
www.ChainReactionBicycles.com