I don't have any terribly inspirational ideas, but do have some mundane ones.
Maybe you need to wait till summer? <img src="/forums/images/icons/wink.gif" alt="" /> (Does spring become unsprung once summer hits, or does it take fall for that to happen?).
Anyway, on to more serious ideas!
Note that I'm assuming that you're working in an environment where your network is limited to the scale you discussed - 7 PCs hooked to a router hooked to a cable modem, and then out to the wild west world (ie: it's not your network after that point).
I am also assuming that other network functions (ie: HTTP / FTP) work fine from this PC.
Also, you can ping / Ping Plotter to other machines on your network, right (albeit your routes will only be one hop long).
1) Make sure you have the "Packet Type" set the same on your main PC as the other PCs (Packet Type is in Advanced Options -> Packet Options). I have a Cisco 678 router here, and I can't ping on one PC while doing it on another PC unless I switch to different packet types. I doubt this is the issue, but is worth a look-see (especially doubtful since PING doesn't work either). Also, check your packet size, Cargo, etc, to make sure it's the same on all your PCs. If you want to be really safe here, rename your PingPlotter.ini (with Ping Plotter closed, of course) to something else (like PingPlotter.ini.bak) and restart Ping Plotter. This will reset all the defaults.
2) Try temporarily removing the NetGear router and connect directly to the Terayon cable modem? Does the behavior change at all?
3) Do you have a dialup account? If you connect via modem from that PC (do you even have a modem on that PC?), can you trace via the dial-up connection?
4) Are you using DHCP on your main PC? Is there any chance the gateway may be different than your other 6 PCs? If you temporarily switch to static IP (in an unused spot, of course) and assign it values the same as DHCP on your other computers (but with a different IP address, of course, one not in use), does the behavior change at all? You want to pick a different IP address than the one DHCP assigned your main computer, and do something like 192.168.1.128 (if you're DHCP server is issuing IPs starting at 192.168.1.2).
5) If you have a different network card laying around, you might try replacing the network card with a different one and allowing DHCP on that different card. Hopefully, the other card is a different brand than the one in your PC now (or you can just leave the other card in the PC so you know the new card has different settings) - as then the settings won't be carried over.
6) Try switching the router port that your PC is plugged in to.
That's all the ideas I have for now. Let me know if any of this jogs it into working (or makes you think of some disturbance that happened 6 months ago where you changed a setting and didn't change it back - or similar).
- Pete