I've tried setting up a Debian Linux box here as a development server. Its IP address is 192.168.0.84, and I can reach it fine at that address. I set up its hostname as "devserver", but it's not being picked up by my DSL modem/router/DHCP/whatever machine. If I want to get at it at "devserver", I have to log into my DSL modem's web interface and manually change the hostname for 192.168.0.84 to "devserver". This works for a few hours, after which the hostname is reset to 192.168.0.84. All the Windows machines here work just fine with it. Anybody have any clues as to why the Linux box isn't playing nice with my router?

You need to explicitly set sending the hostname for the HDCP client. Take a look through /etc/dhcp3/ and the manpage for /etc/network/interfaces.