If you don't know what a media converter is (I've explained it twice in my answers so far (not being snarky, just pointing it out)) it would be like asking me to help you repair a busted head gasket when you don't know what an engine block is. AND we'd be doing it across the Internet, I can't see what your doing, and I don't know the make and model of your car... :)
It's not broken, it's working as designed. Remove the media converter, replace it with a router, and make the router create the connection OR if the media converter CAN act as a router, turn on that functionality, and stop your computer from doing it.
I think I'm confused. The IP address of the ThinkCentre is *.5? What does it show as the Gateway IP address? Or if the ThinkCentre shows that the Gateway IP address is *.5, is that the IP address of the Comcast modem?
Based off of what you just provided, when the Custom is off, the rest of the computers are using self assigned IP addresses. The Custom is assigning IP addresses to everyone (acting as a DHCP server). When it's off, the computers on your network know how to talk to each other (using self assigned IP's), but have no route out to the internet (the Custom is what provides it). The route to the internet is being provided by the Custom in the DHCP configuration.
This means that the Comcast box is likely just a media converter (broadband to baseband) taking the round cable, and changing it to an Ethernet connection. That is fed through the switch into the Custom that then uses PPPoE to create an Ethernet connection. Once it has done that, it hands out IP addresses to the computers on your network.
Is the computer in question (the box on port 4) providing DHCP services? Is the computer (port 4 again) connecting through the Comcast router using PPPoE? If it is your Comcast account may be handing configuration information to the custom build, which then serves the other devices. What MAY be going on here is that the Comcast box is just acting as a media converter.
On the think center on port 2 if you do an ipconfig /all at the command line (assuming Windows) does the gateway address show up as *.4? In *nix based installs you would do ifconfig.