The assortment of cables is either Component or Composite, and both are "old school" connectors. The thicker Component (separate) connectors are the 3 red, blue and green cables. The thinner Composite (merged) connector is the single yellow cable. Both types carry a video signal and require the red/white cables for audio. Since Component has multiple cables, it carries more video information than the sole Composite cable. Of all cables in the AV world, Composite is the most limited cable.
Scenario-1. When you connected the coax to the Dynex and selected "TV" as the input, you were using the tuner inside your TV for a signal. A tuner needs an antenna and your length or coax wasn't a good antenna. No signal.
Scenario-2. Component cables (Red/Green/Blue) can support a full 1080p HD signal, so that was normal. Composite, however, only supports an SD signal, so that was normal. NTSC was the analog TV standard until 2009. Remember the Convertor boxes? We were replacing NTSC with a new digital TV standard (ATSC). When you connected the single yellow cable; your TV informed you of an analog, SD, 480i, NTSC signal from the limited cable.
Scenario-3 and 4. When you connect your Magnavox between your cable-box and TV, I'm not sure but your Magnavox should still pass the signal to your TV. Mouth could be correct with the matching 3/4 output channels; however, this won't ultimately help you because you won't record anything from the cable-box.
Even with old school cables, these newer cable-boxes can detect a recording device and trigger distortion signals while recording. Even with an HDMI cable, your Magnavox supports copy-right protection and won't record anything. These distortion signals are either from built-in Macrovision or Conditional Access Entitlement Control Messages (ECM) technology.
Your "Cisco-straight-to-TV coaxial connection" should have worked, but it read as though you selected a tuner inside your TV as the input. That'd require an antenna. Select the cable-box as the source and set the same RF Modulator Channel.
However, as I noted, your video pirating days are over with the new cable-box.
