By ATSC-C, I assume you mean ClearQAM non-encrypted cable? If so, the procedure is the same for ATSC-C as it is for DVB and ATSC-T.
In my experience, sometimes Tvheadend needs a reminder to scan your muxes for services. To fix this, first I select all of the muxes that have yet to be scanned, click on Edit in the toolbar, and change their status from Idle to Pending. Then, I click the Play icon next to one of the Pending muxes. This will force Tvheadend to scan that mux for services, and if there are other Pending muxes, it usually starts scanning those, too.
Remember though, that most cable in the US is encrypted (which is something completely different than CCI/DRM).
To test your cable connection, what happens if you plug your cable into a TV instead of your tuner card? Does your TV scan and find more than 1 channel?