FLIGHT CREW OF B737-700 FAIL TO NOTE ENGINE BLEED SWITCHES IN OFF POSITION PRIOR TO TAKEOFF. RECEIVE CABIN ALTITUDE WARNING DURING CLIMB.

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PERFORMED CHKLISTS AND BOTH FO AND I FAILED TO NOTICE BOTH BLEEDS OFF ON PREFLT. TAXI OUT WAS VERY LOW VISIBILITY AND WE WERE CHKING WX AND WORRYING ABOUT OTHER ISSUES AND AGAIN MISSED THE BLEEDS ON CHKLIST PRIOR TO TKOF. CLBING THROUGH 10000 FT AT APPROX 12000-13000 FT BEFORE WE COMPLETED THE CLB CHKLIST; GOT CABIN ALT WARNING HORN. TOLD FO TO LEVEL OFF; COORDINATED WITH ATC; AND PUT ON OXYGEN MASKS AND ESTABLISHED COM. PULLED OUR QRH AND USED MANUAL OUTFLOW TO CTL CABIN AND THEN NOTICED BOTH BLEEDS OFF! PUT BLEEDS ON QRH CHKLIST WAS COMPLETED AND DSNDED BELOW 10000 FT TO SILENCE HORN. PRESSURIZATION RETURNED TO NORMAL. TALKED TO FLT ATTENDANTS AND PAX AND EXPLAINED WHAT WAS OCCURRING AND THAT THE SITUATION WAS SOLVED. ONCE WE CONFIRMED PRESSURIZATION WAS NORMAL; COORDINATED WITH ATC AND RESUMED FLT TO BURBANK WITHOUT INCIDENT. THREATS INCLUDED BEING NEW TO CAPT SEAT IN LOW VISIBILITY SETTING. ALSO; ACFT CAME FROM THE RAMP FROM A BRAKE RIDER WHO HAD FOR SOME REASON TURNED OFF THE BLEEDS ON THE OVERNIGHT AT ZZZ. COMPLACENCY OR LACK OF AWARENESS ON CHKLIST AS TO WHAT THE ACTUAL SWITCH POSITIONS WERE AS WE READ THE CHKLIST. NEED TO VERIFY EVERY SWITCH POSITION AS I RESPOND ON THE CHKLIST. NEED TO ENSURE THE FO IS DOING ALL OF HIS PREFLT DUTIES ON MY COCKPIT FLOWS. BE ESPECIALLY AWARE OF WHAT FO IS DOING WHEN IT'S OUR FIRST LEG TOGETHER. LEARNED TO NEVER PAY LIP SERVICE TO A CHKLIST ITEM AGAIN. VERIFY SWITCH POS WHEN READING THE CHKLIST. MAKE SURE YOU LOOK AT THE SWITCH OR GAUGE WHEN READING. ENSURE SWITCHES ARE LEFT ALONE ON OVERNIGHTS BY BRAKE RIDERS.