Ok, no firmware update available for the router, but on a whim, I changed the encryption from WPA+PSK to WPA+PSK+WPA2+PSK2 & now everything works.
I really don't know why it does, but it does

I confess I was unaware of Belkin having a poor reputation for networking, since I've used a G router for years without problem, but this one has been a pain in the proverbial. Thanks for all the help everyone.