You should not need the serial port to access the Internet at all. It makes no difference to the router which port traffic arrives on. The serial ports were used because of their transmission rates and stability IIRC.

There should be three RJ45 ports on the ftont of the router (maybe two). One of these would be used for ingress traffic and the other for egress in your situation, which you mention is a modem. I am assuming this modem is a cable or dsl modem.

You will have to decide which of these port will connect to your ISP and which one will connect to your internal network. It is likely that your ISP connection will be a DHCP assigned address. Unfortunately I am unaware of how to set up a 2500 as a DHCP client as they were never really intended for this purpose and as such this was not included as part of my CCNA training.

I can, however, help you with the static setup to some degree, which will apply to your internal interface. You should run the following commands to set up your internal interface. I am assuming that you can already connect to the router and access the Cisco IOS configuration prompt.

router> enable

This will put the router into enable mode, which essentially allows you to change all the settings on it.

router# configure terminal

This informs the router that you will be changing configuration settings, and is intended as a safeguard against accidental chenges.

router# interface aux0/0

I am unsure of the exact interface name for the auxillary port, however it is labelled "aux" on the front of the router. You can also purchase additional cards for the router. Your other ethernet port will be called FastEthernet0/0, meaning card 0, port 0. If there were two ports on this card, the second port would be called FastEthernet 0/1. A second card would be FastEthernet1/0 and 1/1, and so forth.

router-config# ip address 192.168.1.1 255.255.255.0

This assigns the ip address to the interface

router-config# no shutdown

This will enable the interface that you are currently configuring. It actually negates the "shutdown" command, which is issued to all interfaces by default.

router-config# exit
router# exit

Your settings should now be saved to the router's running configuration. To ensure that, if the router must be restarted, that these settings will take effect again, enter

router# copy running-config startup-config

And your settings should be saved into the startup configuration.

To my knowledge, static routing entries are added automatically for each interface as you configure them. If not, you will need to add them yourself. A similar procedure to this will work if your ISP is using static addresses. If they are using DHCP, you will need to determine how to set up the router to accept DHCP address assignments. I know this is possible but unfortunately cannot remember at this time how.

This should give you a general overview at the very least and get you up and running with this router. I will leave the rest to you to learn on your own. The built in help commands are a great resource to use before you start googling yourself blue in the face.

It has been some time since I have maintained a switch as this. There may be some errors in this post. I'm sure somebody will catch them if this is the case. Just don't assume that everything here is correct. Most of it is, and hopefully all of it, but you should be able to figure out which parts and improvise where you need to.

Hope this helps.