Simply put, don't "merge" the signals. It ain't gonna work.
You might want to spend a little time reading that big book that came with your TV to see exactly what those inputs can be used for.
If you want your TV work, don't "merge" the two dissimilar signals. Feed them, via separate cables, to their respective, separate inputs.
The digital TV input most likely feeds the ATSC tuner. The cable TV input most likely feeds the QAM or NTSC tuner.
Even if my speculation on your TV's architecture is dead wrong, it won't work if you combine them. Betcha It works if you feed them to separate inputs, though.