None of my cable outlets will connect

optimal performance

It should at least receive a signal.

No error codes. We setup the menu on the contour, but when we tried to watch a show, the screen would go black and nothing would come on. It would also tell us to try a different show. We aren’t using a splitter, but I couldn’t get the old cable to disconnect from the outlet to try the new one. It’s frozen from age. We will most likely need a technician, but we just started having a bunch of electrical problems the same night after we tried to hook everything up, so we will need to get that sorted and fixed before we can have a technician out. The modem did connect to one outlet, but it’s all the way at the other end of the house and the signal doesn’t reach where we need it to.

We hooked up the contour to the same outlet that the previous box had been. I’m sorry, I don’t know anything about the cables. But I do know they are probably older than dirt. We weren’t using a splitter for the contour or the modem. We directly plugged it into to the cable outlet. I tried to replace the cable with the new one, but the old one is frozen in place and I can’t unscrew it. However, I tried hooking the modem up with the cable that came with it, and still no luck.

The cables should be stenciled...albeit faded...and it's probably the older RG-59 because it worked with the 10-year box.

I don't know if Cox rewires houses but you could research a local contractor for cheaper.  "Cable Installers near me"

You definitely need to replace the "frozen" outlet due to corrosion.  I wouldn't even recommend an amp in your case.

It's not that RG-59 can't carry the signal...it's that RG-59 can't carry a "clean" signal as far as RG-6.