Ewww! Something died ... (ABS problem??)

Question

Being the owner of a Snow ABS and the customer of a cable Internet provider, I've for years -- about five, to be exact -- had to live with my Web access crapping out at unexpected and always inconvenient moments, causing me to have to upplug the cable modem for 30 seconds to reset, wait another 30 for the modem to reboot and connect to the network then restart the computer.
Some BS about ABS and a glitch related to DHCP lease renewal.
Anyway, this pain the the butt solution has always worked. Until this week. Our cable connection quit on Tuesday, we tried the usual tricks and nothing. Turned off the computer and the modem overnight to try afresh in the morning. No help. Even tried the admin utility to reset ABS, and even unplugged the sucker. Did everything but a hard reset.
Called the cable company to gripe, was told to plug the modem directly into my eMac via ethernet, reset the modem and voila! Internet again. Except this leaves my iBook offline unless I wire it up.
Something between my cable modem and my computer quit working as it has for quite a long time and I'm at a loss to figure out how to get it working again. Please note, I have no wireless signal problems. There's just no usuable connection being sent on either a wired or wireless basis with my ABS in the loop.
Here's how I was configured when this happened. If anyone has any suggestions for what might have gone wrong and/or how to get my iBook back online wirelessly, I'd appreciate it.
-> RCA cable modem
-> ethernet out to Snow ABS LAN port (wireless signal out to iBook)
-> ABS ethernet out to Belkin ethernet router (for additional wired ports to my network for a nephew's sometime's visiting PlayStation, for instance)
-> ethernet out from Belkin router to eMac ethernet port
-> ABS distributes IP addresses to wired and wireless computers, and continued to despite not sending along any connectivity with the IP. Airport Admin Utility showed an IP address coming in from outside.
As I write this post:
-> Cable modem to eMac via ethernet and leased IP address, ABS connected to nothing so no wireless connectivity to iBook.
If I have to replace my ABS with something new, I might consider getting an Airport Extreme card for the eMac then sharing my ethernet connection wirelessly. Another question: if I did that, could I make use of an Airport Express as a network range extender and/or for AirTunes?
eMac 1GHz G4, 160 GB, 1 GB RAM, Superdrive   Mac OS X (10.3.9)   300 GB Seagate external FW 400 hard drive, iSight

Answer 1

Have you tried resetting the ABS? See KB 106602, Resetting the AirPort Base Station (Dual Ethernet).
I recommend that you change your hardware configuration to this:
cable modemBelkin router[LAN] ABS
Enable the DHCP server on the Belkin router. Configure the ABS so that it does not distribute IP addresses.
...I might consider getting an Airport Extreme card for the eMac then sharing my ethernet connection wirelessly. Another question: if I did that, could I make use of an Airport Express as a network range extender and/or for AirTunes?
No you can not use the AirPort Express as a wireless extender when you are using Internet Sharing on your eMac. WDS only works between AirPort Express and AirPort Extreme base station (AEBS). See KB 107454, AirPort Extreme and Express: Using WDS to create a network from multiple base stations.