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The first thing to establish in your case is do your ESCs ( or ESC combo board) have a BEC ( battery eliminator circuit/ its called that because in the old days, the receiver (RX) used to have its own separate battery ) and according to the specs your combo board does. ( what a BEC basically does is take the main battery voltage and reduce it to a stable 5 VDC for aux equipment including the RX)

What RX ( receiver) do you have? Its sound most likely that.
Your connection from the Turnigy Combo to the RX is incorrect. Double check GND,5VDC, SIG
Your FC isn't configured correctly for the RX ( Sbus, PPM .....)
Your RX isn't configured correctly to "talk" to the FC

What type of firmware is on your combo board ( Cleanflight , Beta flight INav or similar)?