B737-800 Captain reported aircraft wouldn't pressurize due to failure of the left pack; the right pack was already on an MEL. The flight crew ran the QRH procedure but was unsuccessful and decided to return to the airport.

Narrative

While preflighting for FLT ZZZ-ZZZ1; I noted there was an MEL 21-XX for R Pack. The FO and myself discussed the MEL; the procedures and restrictions of the MEL. We discussed them again during the threat forward brief lead by the FO (who was PF) noting that this was not an MEL either of us have dealt with and a procedure we've never done before. As part of the after start flow; and before takeoff flow; we noted the Pack light agreed it was associated with the pack MEL. We proceeded as normal. After we took off and I completed my after takeoff flow; I caught that we were not pressurizing. I began trouble shooting the air conditioning and bleed configuration. My first thought was that I must have mis configured the AC and Bleeds as per the MEL procedure which called for a non standard bleed configuration. I reviewed the MEL procedure and confirmed it was procedurally correct. We were continuing to climb and still not pressurizing; so we agreed to stop our climb. We asked for and got clearance for 10;000 (I think we were assigned 16;000' and currently passing 8500'). I then went to the QRH for the Pack light seeing that it had to be a failed pack that was not allowing us to pressurize. When we leveled at 10;000' we got a momentary Cabin Altitude Warning. In hindsight we probably should've dawned oxygen masks; but we were level at 10;000'; closely monitoring the cabin altitude and task saturated with the QRH. We got an immediate decent to 8000'. The QRH procedure was unsuccessful at brining the L pack back online. We followed the procedure to land at the nearest practical airport (back to ZZZ). With the cabin altitude below 10;000' and no other immediate threats; I elected not to declare an emergency. We followed the procedures for a non routine landing; ACARS messaged our divert; spoke with FAs and made a PA to the passengers.The FO made the uneventful landing back at ZZZ approximately 25 minutes into the flight. We taxied back to the gate; deplaned the aircraft; wrote up the L Pack and proceeded to the new gate with our new aircraft. We were able to complete the ZZZ1 turn two hours late; but otherwise uneventfully. My original thought was that we lost the second pack inflight. But after reexamining our steps from the beginning and a thorough review of the MEL; the L pack must have failed on the ground or maybe never was functioning. We miss identified the pack light as being associated with the MEL and not a separate failure of the remaining pack. We spent a lot of time discussing the MEL on preflight. That set up an expectation bias that a light associated with the pack might be associated with the MEL. The thought that we could have had an additional pack failure never crossed my mind. In hindsight it would've been helpful to brief what a loss of the remaining pack would look like and the critical nature of single pack operations (should we even be taking this airplane to ZZZ1?). Some good lessons learned.Cause: Expectation bias associated with MEL; inexperience with this type of MEL and MEL procedures."