My cable company has told me that I can only use their router, so I cannot use the router function of the time capsule.
This is simply not true, and unfortunately, is typical of the mis-information that some Internet Service Providers relay to their customers.
Even if you are using the cable company's router, you can set up the Time Capsule to back up your Mac and also provide a second wireless network that you might use for guests, the kids, or other purposes.
The Time Capsule wireless will run circles around the wireless performance of most routers provided by most Internet Service Providers, so if you find that to be the case, you can use the wireless of the cable company router for a guest network, a kids network, or other purposes. You also have the option of turning off the wireless on the cable company router if you want.
If for some reason you decide to use the cable company router for your wireless network, and you don't want a guest network or second wireless network, then the wireless function of the Time Capsule can be turned off with just a few clicks.....and the device will perform as a simple hard drive, backing up your Macs over the cable company wireless network.
Since it is clear that your ISP will not help you as far as integrating the Time Capsule, you might now decide what it is that you want to do, given the options that we have mentioned.
If you want more help, we'll need the make and model number of your cable company router to be able to provide the detailed steps to set up the Time Capsule.....no matter whether you you decide to use the Time Capsule wireless capability or not.