Call the cable company and complain.
If you are paying for both services, and the put the splitter there, it is their problem, not yours.
If you are not paying for TV service , they will gladly provide you with TV service for a fee, and adjust the signal so that both function properly.
There is no free cable TV in the US, free TV is only through Over the Air.
Whatever you are getting with the TV now, will be gone shortly, since FCC allowed cable TV providers to encrypt everything.
6 TV's in the house on FiOS and we only pay $4.99/month to connect them all!!! Power to the CableCard and WMC7!!!