1st thing to check is with your satellite receiver hooked up, plugged in, and on, take a voltmeter, set it to DC. Disconnect the coax at the DirecTv antenna. Place one lead on the center conductor of the coax and the other lead on the threaded part of the coax connector. You should have a reading of approx 13VDC or 18VDC (depends on which transponder or channel). If you do not have either of those voltages, cabling is not correct.
The round discs on the antenna are called LNBs (Low Noise Blockers) and are active devices (circuit boards requiring power). The satellite receiver (known as an IRD) provide this voltage. Most standard coax splitters do not allow this DC voltage to pass through them. An A/B switch may not allow DC voltage to pass either. Common cable TV does not want that voyage on the cable. Your on board TV antenna most likely has an amplifier in line. Depending on the type of TV (off air) antenna, there may be 12VDC voltage between the switch and the active TV antenna (amplifier is a circuit in the antenna on the roof).
Bottom line, make sure you have 13VDC or 18VDC at the directv antenna. With the direcTv cables disconnected, there shouldn't be any voltage on any cable.
In my last TT, it took me a little while to figure what the factory had done. I have been a marine electronics tech and a communications tech for many years. I have installed many, many, satellite systems on yachts and RVs.
Most of the coax connectors from the factory were of the screw on type and were loose.
2013 Cardinal 3800FL
2009 GMC 3500HD CC LB SRW