Hopefully the formatting there makes sense! The Vista machine is connected to the Linksys router.
Anyway, from my Vista machine, I can see the Linksys router and that is all, unless I go into the router setup, where I can see the Netgear router on the IP table. And from the Ubuntu machine, I'm not sure what I can see since I'm still learning what is where in the KDE GUI, but I am able to access the internet through the above mess.
When you stack the two routers, Netgear WAN port to LinkSys LAN port, you've effectively hidden everything connected to Netgear as Netgear NAT'ed out all packets going out of its WAN port. That's why your Vista PC cannot see Ubuntu machine. But Vista should be able to see your Netgear router.
Your Ubuntu machine should be able to see Vista if you use Vista's IP address directly. On Ubuntu, 'netstat -r' will show you its routing table.