Ok, take a couple deep breaths....
First, forget about using the word "NIC" - as that does not really apply to hardware in the world of Cisco. You stated that your new router only has one ethernet interface. Ok. Besides the ethernet, AUX, and Console ports..... do you see ANY other interfaces on it at all?
Next, you say that your current router has two "internet NICS". We need to determine what type of interfaces those are. So let me ask you this. What do you use for your internet? DSL? T1? Also, you said TWO interfaces are "internet NICS". Are you telling me that you have TWO DSL lines, or TWO T1s (for example)..... or do you really have ONE DSL and ONE ethernet cable? My guess is that you actually only have one internet interface, and one LAN interface. Let me know what type of router your current one is as well.
Judging by the additional information you should provide me, there are a number of solutions. Wost case scenario - you will have to purchase a module for your new 2610 that will handle the internet duties. A module is basically a hardware card that slides into one of those empty slots on the router. It is comparable to a NIC card. Best case scenario - we can utilize the "IP secondary" feature on your router.
Whatever happens is going to require a certain level of Cisco technical expertise. By all means I am not trying to disrespect you at all (please dont take it that way), but experience with Cisco equipment is recommended....even for simple projects such as this.
