There used to be a solution to this with Windows XP, involving recreating a user account in Windows, and a solution for Windows 7 by doing something with a registry entry, but from what I gather any solutions are hit-or-miss, sometimes they work and sometimes they don't. This is one of the most crazy maddening errors you will ever see in Windows, and even Microsoft themselves would just take you through all the same things Cox probably already has. I tried a search and get a lot of non-helpful banter and speculation, with possibly some solutions after looking at about 15 pages. Sooo...do a search on the web for Enter Network Password solution and try every solution you see that actually gives you the steps to do (which is very few, there sure are a lot of speculative morons on the internet, e.g., "It could be this, it could be that" but not offering any concrete solutions LOL).
Just to note, this is NOT a Cox issue. This is a Windows issue. Your last step if you can't solve it is to do a backup of your files and wipe the windows box and do a reinstall of the thing from your recovery disk or partition, and make sure to do a full clean install, not just a "repair windows for me". I have found that with stubborn Windows issues if you spend more than 3 hours and still can't find the solution, it's better to just do a backup/reinstall and stop beating your head against the wall. You're just money ahead time- and frustration-wise to do that after a certain point and be done with it. I know that's not a good solution for everyone, I am comfortable with it because I've been building computers for years, but if you're not maybe you have a geeky friend who could do it for you, or you can pay a computer shop about $150 to do it (there goes all that money you "saved" on the cheap windows computer).
Or just buy a Mac and get around all that nonsense (the issue has never occurred using Outlook for Mac because again, this is a Windows issue, not a provider issue). I know, not a lot of help either, but maybe at least a direction, sounds like Cox has done all they can to help you.
There was a similar issue plaguing Outlook 2010 users who used Hosted Exchange mail, that tossed an error "The action cannot be completed. The connection to Microsoft Exchange is unavailable. Outlook must be online or connected to complete this action" (Even though it is connected online of course) and it was very frustrating for tons of users, although there was a better fix for that one.