A B737-300 Flight Crew reported loss of cabin pressure. They ran the procedure; declared an emergency and diverted.

Narrative

Day 3 of scheduled 4-day trip. Leg was #4 of a scheduled 4 on that day. Bleeds off; max power takeoff due to wet/good conditions at our departure city. After takeoff; bleeds reconfigured at level off at 3000' MSL; APU off by 7000' MSL. Uneventful climb to FL320; and on top VMC by 17;000' MSL. After being established at cruise at FL320 for approximately 10 minutes; Cabin Altitude Warning horn sounded. QRH immediate action procedures accomplished; donning masks and establishing communications. Verified cabin altitude was at 10;500' and climbing at 500 fpm. Coordinated with ATC for a descent and Captain flew and handled radios while First Officer accomplished QRH procedures. Bleeds were verified in normal position along with PACS. Of note; old style pressurization panel in the -300 aircraft. Following QRH; attempted to control pressure using DC MAN controls; but cabin altitude would not get below 10;400' despite valve indicating full closed. Valve moved very little with manual switch due to it indicating almost full closed prior to initiating the QRH procedure. We determined cabin altitude was not controllable; an emergency descent to 10;000' MSL per checklist and coordinated a divert to the closest suitable airport; approximately 45 NM away. Both QRH procedures for emergency descent and pressurization were accomplished. Visual approach aided by ILS accomplished. Normal After Landing checklist and flows accomplished. At gate; cabin altitude still at 2000' MSL despite manual outflow valve being in open position. First Officer had to manually open outflow valve using DC power to slowly bleed off pressure to open main cabin door.