I think maybe the c7770b, which is, I believe, the older of two versions of the Designjet 500 42, is just too old. The HP site takes me to a page when I search for drivers with that model number, but I get the problems I've described.
I tried updating the firmware. Everything works until the final step, and it just says it failed to communicate with the printer.
"HP Designjet 500 42 by HP" driver seems unwilling to upgrade beyond driver v6.07, data file version v2.1.
The darn thing is old--first manufactured in 2000. It may be time to take it out back and shoot it.
Actually, I scavenged a old iMac yesterday, and I suspect that will work flawlessly with the "obsolete" printer. I darn near know it will, actually, because I used to have an iMac of the same generation/OS, and it "just worked".
Actually, I've NEVER gotten this thing to print in Windows. There's probably some way to edit some file and make Windows think it's a slightly newer model, but one can only waste so many thousands of hours tilting at a given windmill.
Thank you very much for your help, though, Derryck.