Masquerading behind router - no email

[sans peur]

Greetings,

My main machine has a cable modem connected to a static IP. My linux machine is
masquerading behind the other machine through a router that is running on the
other machine.  I can access the internet fine from the linux machine at
192.168.0.1.  www, ftp, and telnet all work fine through the router to the linux
machine.  However, I cannot use sendmail.  Sendmail gives me an error saying
that the domain of the linux machine is unknown. True.  Do I need to configure
BIND in order to have sendmail recognize the domain name as valid on the linux
machine?

resolve.conf has:

search mydomain.com
nameserver <quad IP for my ISP's nameserver 1>
nameserver <quad IP for my ISP's nameserver 2>

All internet transactions work great using the bogus IP address since the router
at the main machine converts through the gateway to the static IP -- no problem.

Do I need to run BIND in some limited way (cache only nameserver) and specify
forwarding for DNS at the ISP nameserver address in order to get sendmail to
recognize mydomain.com?

Any help would be appreciatied... 
thanks,
SP