welcome to LQ.
1. why is the system you are currently trying to instal debian on unable to connect to the internet if it has a NIC? just plug it into the ISP's router/modem/ or your wireless router, it should have a few ethernet ports no?
2. if the only way to get access is to setup DHCP via the other computer then you will be dealing with double NAT. this can cause connection issues. please keep that in mind.
that was a fast google search: "debian howto share internet connection"
3. also as mentioned you might consider not using the netinstaller for Debian. I know it is the preferred way, but... if no connection, then no connection.