Kappy is dead on correct about Bridge Mode as a requirement for the Time Capsule.
Do you know how to check to see if the Time Capsule is configured this way?
Next question.....you really should not try to have two wireless networks....one Arris and another Time Capsule.....unless it is absolutely necessary. Two wireless routers in close proximity can create wireless interference effects that can cause problems with either...or both...networks.
Best to turn off the wireless on one router to keep the chances of wireless interference between routers minimized.
Are both the Arris and Time Capsule providing wireless signals?