B737 flight crew departs SLC with a PACK on MEL after rumbling noise is heard during taxi and ice in PACK is suspected as the cause. Cabin altitude begins to rise with single PACK operation at FL250 and crew elects to use the deferred PACK rather than descend. This works and flight continues to destination.

Narrative

As we taxied to the runway in SLC; the Flight Attendants called to inform us of a loud noise coming from mid-cabin. We pulled over at the end of the runway and I; the First Officer; went back to the cabin to investigate. After some troubleshooting; we discovered that the right pack was the cause of the noise; and the noise would stop when that pack was shut off. We contacted our Maintenance Controller who felt that the cause was ice in the air cycle machine. They deferred the pack and we were refiled for FL250; single pack. Everything was normal; pressurization wise; as we climbed and leveled off. Soon after leveling off at FL250; I noticed that the cabin altitude was still climbing at 500 FPM and was nearing 8;000 FT cabin altitude. We verified that the outflow valve was closed and decided that our only recourse was either to descend over very high terrain or to turn the deferred pack back on. The Flight Attendant stated that the noise was gone. The cabin altitude was restored and we decided to continue at FL250 rather than divert when all indications were normal.