CRJ-200 Captain reported loss of the sole operating air conditioning pack resulted in loss of cabin pressure control. The flight crew requested priority handling and performed an immediate descent to 10;000 ft. An air turn back and precautionary landing were performed at departure airport.

Narrative

We had a L Pack Hi Temp Caution Message on the ground in ZZZ. So we called Dispatch and Maintenance. Did all the paperwork and deferred the Left Pack. We took off with a single operative pack; the right pack. Swapped the bleeds to the engine from the APU. Had a feeling there was an issue so we level off at 5;000 ft. I re-transfer the bleeds from the engine to the APU and then back to the engines; thinking that one of the values got stuck. It seemed to have cleared up the issue. We continued the climb to 15;000 ft. Around 10;000 ft. we got a CABIN ALT WARNING message. The First Officer (FO) continued flying and I pulled out the QRH. While running the QRH; we ended up getting a CABIN ALT WARNING message around 13;000 ft. We put on our oxygen masks; established communication between the pilots; requested priority handling; started descending at 250 kts. down to 10;000 ft. We then did the QRH procedure for the warning; but we knew the pressurization issue wasn't due to structural damage and that the door was safe. We got down to 10;000 ft. quickly so we didn't drop oxygen for the passengers. Tried to manually pressurize the cabin but it wasn't working. At this point the FO and I realized that the Right pack switch was still pressed in (On) but the switch itself was illuminated and said the Pack was OFF. We never received and ECIAS status message telling us the right pack is off only have the left pack off showing on the ECIAS status messages due to the MEL for the L PACK HI Temp caution message that occurred on the ground. Did the QRH for unpressurized Flight Procedure using the Packs OFF scenario. Continued the rest of the flight unpressurized at 10;000 ft. all the way to ZZZ1. There was no issue landing and getting to the gate. The Flight Attendant (FA) mentioned to the FO and I that none of the passengers even noticed there was an issue and he only knew because I told him. It all ended safely with no problems.We now believe the cause was that the Right PACK failed after takeoff and before we got to cruise; causing us to be unpressurized due to the fact we had the left pack off due to the MEL requirements after getting the L PACK Hi Temp caution message. We didn't notice the right pack was off because we never received a right pack status message.To pay closer attention to all the control panels and what information they are providing us with and not relay on just what messages we see the plane tell us.