Romex is a brand name, but commonly used to refer to NM (non-metallic) sheathed multi-conductor cable for 120V/240V wiring.
What you have in the picture are 3 low voltage (i.e., telephone and/or networking) cables. Red/Green/Black/Yellow is extremely common for 2-pair telephone cable (Red/green for the first pair, black/yellow for the second pair, used for either two phone lines or a phone system with one pair for voice and one for control signals).
So none of that is what is commonly referred to as "Romex", and none of that should have anything to do with your 120V circuits. The insulation is almost certainly not rated for 120V, and the wires are way to small for even a basic 15A circuit. In addition, low voltage cables (phone, network, cable TV, burglar alarm, etc.) are never supposed to be in the same boxes, conduits, etc. as 120V circuits.
My best guess is that you have a loose connection somewhere near the data receptacle that you worked on, and now it has come apart, breaking the circuit. But it is also possible that it is a coincidence and totally unrelated.
GFCI is often a factor, but if a GFCI receptacle works then anything connected by the LOAD terminals should work as well. Possibilities (GFCI or not) include:
- Loose screw connection
- Bad backstab (and if you find one, replace the receptacle or at least move the wires to screw terminals)
- Loose wire nut
- Mouse chewed through a cable (evidence will include a dead toasted mouse)
- Flipped switch - a switch can control a receptacle or a whole chain of receptacles. Not generally recommended, but stranger things have happened.
Keep hunting. And along the way, make a map of your circuits for the next time.
