B737-700 Captain reports cabin altitude warning horn climbing through 13;000 FT on a ferry flight. Packs and bleeds are verified on and the outflow valve is manually positioned toward closed. When the climb is resumed the cabin warning again sounds and the crew continues to destination at 10;000 FT.

Narrative

We were on a 45 minute repositioning flight with only 2 pilots on board. No flight attendants; no passengers. On climbout through approximately 13;000 FT; the cabin altitude warning sounded. After performing the immediate action items; I leveled the aircraft off just below 14;000 FT and requested a descent to 10;000 with ATC. ATC immediately issued this clearance; so I felt it unnecessary to declare an emergency. After leveling at 10;000 FT; we ran the QRH checklist. We double checked that both the bleeds and packs were on; which they were. We changed the pressurization controller to Manual and closed the outflow valve. The pressurization seemed to be coming under control. Once we had established a 1;000 FPM cabin descent; we were confident we could maintain pressurization control manually; so we requested a climb to our cruise altitude of 30;000. We were cleared to climb. Again out of 13;000 the altitude warning horn sounded and we again donned our O2 masks. We descended again to 10;000 and remained at 10;000 throughout the duration of the flight. The remainder of the flight was uneventful; and we landed without incident. With the outflow valve full closed and both packs showing good pressure; we were unable to control the pressurization of the aircraft. It was as if a door was open or a window had blown out. One way or the other we were expecting to find a large hole somewhere on the aircraft.Probable mechanical failure or snow packed into the outflow valve. There was a strong wind blowing drifting snow in the direction of our outflow valve as we sat at the international gate at the departure airport. Other interesting things which happened during this event include our inability to contact dispatch via radio (we tried both frequencies) nor ACARS. ACARS was NO COMM. Possibly this is because we were only at 10;000 feet. Nevertheless; we were pretty much on our own with the decision to continue rather than turn back. We decided continuing was a safer option; as the winter storm we were trying to escape from was just bearing down on the departure airport; and the FMS was showing us landing with 8;000 LBS of fuel after setting the cruise altitude to 10;000 in the FMC.