I presume you're using the Netgear in UPnP mode right? I don't use windows XP so I'm not sure about the windows UPnP setting. But check that the UPnP setting is setup properly for the other accounts: http://www.alloy.com.au/support.asp?TID=229
I'd have thought that setting would be universal however for all users.

I do know Cox are reknown for p2p shaping but they don't apply it to all users.

Your Java version is a little old.

In the other user accounts, try deleting their LW Preferences folder whilst LW is closed; instructions here: Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.)

Upon opening, set LW so it doesn't start on startup. LW's menu bar, Tools>Options>Connections & disable connect on start up. Then next time opening LW let it settle for 5-10 mins, then go to File menu -> Connect. Give it plenty of time to connect.

I presume you configured XP firewall for each user?! Firewall configuration instructions (click on link). This can be found in the Control panel I believe.

Do you have a separate installation for each user or use shortcuts? You can simply use shortcuts from the single installation of LW. Send them to the user account desktop or start menu > Programs folder for that account.