A CRJ-200 Captain reported that after being dispatched with one pack inoperative; the remaining pack had an over pressure fault and shut down; resulting in loss of pressurization. An emergency was declared; a descent initiated; and the flight diverted to the nearest suitable airport.

Narrative

We took off [and] had a right pack overpressure. We completed the QRH procedure [and] leveled off at FL240. Approximately 5 minutes later I noticed a status message of 'Right pack off' and the cabin altitude was climbing. I used Captain's authority to quickly reset the pack to stop the rising cabin pressure; it didn't work. I again used Captain's authority and tried the left pack to stabilize the rising cabin pressure. When that didn't work I told the First Officer to ask for lower. The lowest altitude ATC could give us was 15;000 FT. Soon after that the 'cabin alt' caution message appeared. We donned our masks and completed the QRH procedure. I didn't ask for an emergency descent because we were already on our way down. We deployed the cabin masks because we couldn't get below 10;000 FT for a long period of time.While the First Officer was completing the QRH; I asked for vectors to the nearest [suitable] airport. I also declared an emergency. We made sure the flight attendants and the passengers knew what was happening before we dropped the masks. Once below 10;000 FT; I called for O2 off and we landed without further incident; although it's a pain to actually use the masks for an extended period of time. Also; we got a 'crew O2 lo' caution very quickly after donning the masks. I believe that there was a faulty ECS. The pack turned off; it did not over-pressure or over-temp. The right tenth stage was closed and wouldn't open and the isolation valve [closed] even though the left tenth valve was open and had pressure. Suggestions: don't dispatch flights over mountainous terrain with only one pack.