I am going to explain this as well as I can without pictures, (though it would be easier) Since the question was asked about a cable modem I will explain using the term cable modem, though the same explanation can be used for DSL Modem, Broadband, etc.
For our purposes, there are two sides of IPs - External (WAN) and Internal (LAN)
*(WAN) is Wide Area Network. This is the IP that is on the proider side of your cable modem and is shown when you look at IPchicken,
IPBurger, etc. It can be
Static (can't be changed-the same for the life of your account with that provider.) or it can be
Dynamic (It is "leased for a certian number of hours, days, etc and will change periodically on it's own or you can change it using methods explained in other threads.) Your WAN IP may look something like this: 98.172.166.235
*(LAN) is Local Area Network. This is the IP or IPs that is on your computer side of you cable modem. If you just have one computer plugged into the cable modem, you computer IP may be: 192.168.1.1 or something like that. If you have a router, that device is plugged into the cable modem where you would usually plug in a computer. Then the router splits or shares the internet to other computers that are connected to the router. So then if you have 4 computers, they may have IPs like: 192.168.1.1, 192.168.1.2, 192.168.1.3, 192.168.1.3.
When we talk about ebay seeing your IP, from this example, they would see the 98.172.166.235 - no matter which computer you logged in with. They don't see your internal IPs.
So, if you have a dynamic External (WAN) IP from your cable provider, and have a stealth account on each one of your 4 computers, you would have to use the knowledge here in other threads and change the IP before logging in to each stealth account or they will become linked.
The above info are for most end user situations but there are variables. You can buy static IPs from you provider so each PC can have it's own external IP. The problem I see with that is that the IPs will usually be in a numerical series range. I think that would look odd to eBay. Also, if you have a stealth account get suspended, it's IP that you bought would be no good anymore, and not easily changed with your provider.
I hope that I made a little headway explaining this topic.
*Note to my other computer peers - Yes, I know that there is a lot more varialbles, definitions, and explanations. I'm just trying to dumb this down enough so non-techies can understand it.
Computer do it? 
I have a macbook, Asus notbook, IMAC and a custom built pc. I am thinking the macbook could be used as 2 computers because it has 2 operating systems on it. There is mac OSX and windows xp installed on different partitions. This is the perfect amount of computers for the amount of stealth accounts i have so should i just use 1 ebay account per computer?
I now realize i have possible linked many accounts!!! @!$#!!!!!!!!!!!!! Soon as the listings i have up are finished i am gonna let them lie low for a loooong time. 
