think he means a consumer level router with a built in 4 port switch.
the dual NICs is the problem. There was another poster wondering about Dual nic motherboards and what to do with the second NIC. There's not much except to configure the computer as a router itself to utilize the second NIC. That can chew up system resources when the computer has to act as a router.
A printer with an ethernet port should be plugged into an ethernet switch [a LAN port on the consumer level router or a 10/100/1000 switch] and assigned an address. [see below for addressing on the second NIC].
The reason your having trouble connecting to the internet when you hook up both the printer to a NIC and your internet connection to the second NIC is that the computer doesn't know where to send the traffic. I'll bet it sends internet requests to the printer when it's plugged in.
The first NIC needs to have a static address, with the default gateway as your consumer level router and DNS is your ISP DNS.
The second NIC needs a static IP address on a different subnet with no default gateway and no DNS servers listed. This second NIC would be plugged into a switch [not the consumber level router built in switch] where all other computers and ethernet printers also plug into. This is how you setup your computer to act as a router. All hosts would then have your 1st NIC which connects to the router as their default gateway. That NIC then knows to router all traffic not destined for the LAN out through the default gateway and to the router which then forwards traffic to the internet. Then run the Internet Connection Sharing wizard so that other computers then can utilize your comp as their router out.
the problem with this setup is that the dual NIC comp must be on for other hosts on the network to get to the internet.