Air carrier 737-300 Captain reported a loss of pressurization at cruise altitude and returned to the departure airport.

Narrative

During cruise phase of flight; flight crew observed MASTER CAUTION illumination with SYSTEM annunciator light on first officer side illuminate AIR COND and illumination of DUCT OVERHEAT on overhead panel; indicating on the left side; immediately followed with illumination of CABIN ALTITUDE annunciator with sounding of AURAL warning intermittent horn alert.Flight crew immediately responded with action of donning the oxygen mask with 100 percent oxygen and establishing crew communication and completing the rest of the memory items for the Cabin Altitude Warning or Rapid Depressurization check list per the QRH.Flight crew noticed Cabin Altitude pressure indicator; indicating a cabin pressure of 13;000 ft. with a differential pressure of about 1 and a cabin climb rate of 500 ft. per minute.I instructed the First Officer to get the QRH and run the Cabin Altitude Warning or Rapid Depressurization check list. The First Officer informed me that when he closed the outflow valve switch; that the cabin wouldn't pressurize. I reacted by [requesting priority handling] with ATC; informing ATC that we will be descending and that we would like vectors to return to the origin airport and informing ATC the nature of our [problem] with pertinent information.After receiving the altimeter setting from ATC; I initiated an emergency descent completing the memory items with First Officer verifying actions with QRH Emergency Descent. Upon reaching a safe altitude with a cabin altitude pressure indication of below 10;000 ft. cabin altitude pressure. Flight crew completed the QRH check list.With the Captain performing flight and ATC communication duties; First Officer continued with the Duct Overheat QRH check list to completion. While enroute back to ZZZ; I informed Dispatch that the flight [requested priority handling] and are returning back to ZZZ. Our flight returned to ZZZ Airport with no further incidents.