FLC OF MLG ACR ACFT FAILED TO TURN ON PWR FROM THE ENGS FOR AUTO CABIN PRESSURIZATION DUE TO GND DEICING DISTR.

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AFTER DEPARTING THE GATE IN CLE WE DEICED THE ACFT AS PER OUR OPS MANUAL. THE COPLT TURNED OFF BOTH PACKS; HE COMMENTED THAT HE NEEDED TO TURN THE PACKS ON AFTER THE 1 MIN WAIT TIME. WHILE WAITING WE RECEIVED TAXI CLRNC AND STARTING A TAXI ON THE ICE AND SNOW CONTAMINATED RAMP. ATC GAVE US CLRNC TO FOLLOW TFC; AFTER LOCATING THE TFC WE DID AS INSTRUCTED. THE SNOW WAS ACTIVELY FALLING AND THE TAXI CONDITIONS WERE NOT THE BEST. WE RAN ALL CHKLISTS; INCLUDING THE DEICE HOLDOVER CHKLISTS. FO RECEIVED CLOSEOUT INFO AND COMPUTED A V1 CORRECTION. AFTER ALL CHKLISTS WERE COMPLETE; WE DEPARTED CLE WITH ANTI-ICE ON. NO PROBS UNTIL REACHING 21000-22000 FT WHEN WE RECEIVED A CABIN ALT ALERT ON OUR MFDU. WE ASSESSED THE PROB; TRIED TO 'CATCH' CABIN WITH MANUAL CTL BUT NO HELP. I ASKED COPLT TO ASK ATC FOR A LOWER ALT WHICH WAS GRANTED -- 11000 FT. WE STARTED DSNDING AND THE PAX MASKS DEPLOYED WHEN CABIN REACHED 14000 FT. THE CABIN CLBED TO 14500 FT PRIOR TO US INTERCEPTING THE CABIN IN OUR DSCNT. WE RECEIVED FURTHER DSCNT TO 10000 FT AND TOLD PAX TO DISCONTINUE USE OF OXYGEN. AFTER RUNNING ALL CHKLISTS; I FINALLY NOTICED THE PACK SWITCHES OFF. THE OFF LIGHTS WERE VERY DIM; AND IN NO WAY WERE OBVIOUS THAT THEY WERE OFF. I TURNED THEM BACK ON AND REPRESSURIZED THE CABIN. WE CALCULATED A NEW FUEL BURN TO RDU; CALLED OUR DISPATCH; TOLD PAX PROB WAS FIXED AND THE ACFT WAS WORKING THE WAY IT WAS DESIGNED. WE CONTINUED TO RDU WITH NO OTHER PROBS.