Need to connect my old Linksys modem to a new Motorola SBV5121 cable modem.

Try a different ethernet cord if you haven't already.

update the router firmware
You can do it via Linksys or as many of us have done, use this 3rd party firmware
http://www.dd-wrt.com/site/support/router-database

You have two ways on how you can get other computer online through this router. First, you can wired them (using an Ethernet cable) to one of the Ethernet ports on the back of the router. They are the ones labeled 1, 2, 3, and 4.

Second is through wireless, but those computers that will connect through wireless must also have a wireless adapter to be able to pick up the signal that this router is broadcasting.

Connect the cable from the LAN port on the DSL modem to any of the 4- LAN ports on the Linksys Swicth (not the port Labelled Internet), then from any of the remaining 4 ports then connect your computer. Also try using a cross-over cable to modem from the DSL LAN port to the Linksys.

First of all: it would be good to know which devices you are using. This would help to be more specific.

But anyways:

1. Connect a normal Ethernet cable from your DSL or Cable modem to the Internet (or WAN) port of your vonage router.
2. Then connect another Ethernet cable from one of theLAN ports of the vonage device to the Internet (or WAN) port of your Linksys (The one that is separated from the 4 LAN ports.)
   
3. Make sure that the Linksys is set to DHCP (Dynamic IP Address), soit can get it's IP address from the vonage router! (Look at your manual. If you don't have one, you can get it here. Choose the right version number - you can find that on a sticker at the bottom of the router - and download the user guide)
   
4. Connect your computer to one of the LAN ports on the Linksys.

If you have any more questions or this desciption is not clear to you,just come back here and leave a comment - I'm happy to help.

If you are not using a router, you probably have one built into your modem provided by your ISP. You would need to either reply back with the make and model of the modem or contact your ISP and ask them how to do it.

Normally you would connect your DSL or Cable Modem to the WAN or Internet port of your router. Then you will connect your Desktop and/or laptop to one of the available switch ports. They usually have 4 of them. You use standard ethernet cables for all of the connections.

Ok to start the yellow ethernet port should be connected straight to the Linksys router in the ethernet in port. Then you connect the cmputer to one of the other the 4 ports on the back of the wireless router. wala you shouldn't have any more trouble after that.

your SPA2102-R seems to have one ethernet connection and one internet connection.
your WRT54G-TM seems to have one internet connection and 4 ethernet connections.

What you are trying to achive is; plug a ethernet cable into the ethernet connection on your SPA2102-R then plug the other end into the internet port of the WRT54G-TM

hope this helps, I have assumed that you intend to use a DSL broadband supplier not ADSL.

if you are changing service from DSL to ADSL then your WRT54G-TM needs to be first in line configured and working. then plug the internet port from the SPA2102-R into any of the WRT54G-TM ethernet ports.

This web page has a wonderful graphic step by step to use port forward for your linksys router:

http://portforward.com/english/routers/port_forwarding/Linksys/WRT54G/default.htm

Hope this helps.