If you go to you should get at least a signal page and possible a log page you can post, I can help you more from that.

Modems can have issues for a variety of reasons, but it sounds like the more plausible one, from what I can guess ,is your upstream is having problems and the extra split is pushing it over the limit.

Also when you have the single line connected, can you perform a
ping www.cox.net -n 150
from the command line and post just the results,