Q400
Flight Crew Air Transport Pilot (ATP)
Workload; Situational Awareness; Distraction
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Became Reoriented; Flight Crew Overcame Equipment Problem
Aircraft; Human Factors
After [bleeds-off] takeoff while performing the after takeoff items; we received a clearance to 'resume the arrival'.  We got this clearance just before I turned on the bleeds.  I then reached across to program the First Officer's FMS.  I then made a mistake during the programming; and had to take a little more time to rectify the error.  Once I had gotten that corrected; I reprogrammed my FMS.  We then received another climb clearance; which I promptly put into the alerter.  At this point we were about to enter the clouds and icing conditions; so I selected on the icing equipment.  Needless to say; I never got the bleeds selected on; and apparently never finished the checklist.  On descent at about 10;000 ft we received a cabin altitude warning light.  We immediately realized the bleeds were off; and selected them on.  We were already in the descent to 7;000 ft; and before we could complete the emergency checklist; the light extinguished.
[Narrative 2 provided no additional information]
A Q400 Captain reported high workload after takeoff and failure to open the pneumatic bleeds; resulting in the aircraft's failure to pressurize.  When bleeds were opened; normal operation resumed.