Phone Service Down For a Week

"I was told by support to "unplug your phone from the modem"

Sounds like they might have seen your phone in "PLO" which is when the modem detects the line open with no one on it for a set amount of time. This is done to keep a line from staying open if the other party hangs up and you don't.  The procedure to correct this is to disconnect all lines and wait for the modem to detect the closed line and to restore dial tone. I assume you have your phone modem connected to all the jacks in your house. If so, any phone in the house, or even a damaged wire or jack, can cause the issue. 

I would suggest finding your phone modem (probably a DPQ3212) and disconnect the phone wire from the back. Let it sit for 15min then try connecting a phone directly into the jack you had just unplugged. If you still don't get a dial tone, try resetting the modem with the recessed button on the back next to the coaxial connection. After resetting the modem, wait a couple minuets and try again. Sometimes you have to turn the phone on/off a couple times for the modem to establish the line. If you still don't have dial tone then, something is probably broken with the jack. You could ask Cox to try provisioning the line to jack 2 on the eMTA, but that would only be a temporary fix. 

If you do have dial tone back at that point, try hooking the phone line from the modem to wall jack and see if the other phones have dial tone. If all you hear is a open line, then something in the house is keeping the line open. Try unplugging anything that uses a phone(fax, security system, phones, etc) and then reconnect them one by one, listening for dial tone. When you get to the device that does not have dial tone, most likely that is the culprit. Check the phone cord and jack for that phone. If nothing else, you can help isolate the problem for the technician to fix when he comes. Good luck.

Thank you for your suggestions.  I did try this and now I do have a dial tone after entering a number but then just dead air.  Although I did not change any of my phone set up, I did move my wireless printer from a different room to beside the area where I have the phone.  It is a printer/fax machine.  I have never used the fax. It has never at anytime been connected to the phone.  I unplugged this device and moved it back to the other room. Then I went through the disconnect process again with the phone and the modem and it is still the same.  I can now hear the dialing but then dead air. I don't know what you meant by "wall jack".  When I set up the phone and had it working I was told I would never need a wall jack, just run the cord from the phone jack to the modem jack.  When you say something is probably broken with the jack, which one are you referring to?  The one on the modem or the one on the phone? There appears to be nothing wrong with the actual cord so I am at a loss as where to go from here.

Bryn9 said:
It has never at anytime been connected to the phone.  I unplugged this device and moved it back to the other room.

As long as you don't have a phone cord going into the printer/fax, you can put it anywhere you want.

Bryn9 said:
 I can now hear the dialing but then dead air.

Can you receive calls if you call your home phone from your cell?

Bryn9 said:
I don't know what you meant by "wall jack".

Bryn9 said:
just run the cord from the phone jack to the modem jack.

Sounds like you never used a wall jack. How you have it configured works when you only have 1 cordless phone base.  Some want all the phone jacks in their house to function, and connecting a phone line from the modem to a phone jack in the wall does this. However, if you don't use it this way, stick with that. It simplifies the problem. 

BTW, did you reset the modem after getting dial tone? If not, try that. Seems like your issue is similar to this thread.