Limit switch is good but no heat
The limit open error code, simply means that the limit circuit is open. This could be an open limit switch (of which there could be more than one), a loose/disconnected wire, a bad control board, or some other break in the circuit.

Most systems apply 24V to the limit circuit, and if they don't detect ~24V on the other end they throw the error. 

Locate the schematic, then trace the circuit to find the break. Without knowing the make and model; or having the schematic, there's not much more help I can provide.