After the 10.6.1 update, the drivers did install. That did not fix the problem. I finally figured out that for reasons which are beyond me, the HP 4200 was insisting on living at 192.0.0.192, an IP beyond the range of the Netgear router. Despite enabling DHCP, this is the IP that kept coming up. Therefore, nothing would talk to the printer.
I checked the router, and everything else was in the range of 192.0.0.1-6. There were several unassigned addresses, I picked 192.0.0.4 because the printer was plugged into port 4 on the back of the router.
I went to CONFIGURE EIO 2 on the printer and looked for something to manually set the IP address. I put this IP address in and things are good so far. It's not clear to me whether turning the machine off would require resetting the number. It's also not clear why the machine keeps reverting to BOOTP instead of DHCP and getting an IP number automatically.
However... the printer now prints.