LEAR 31A FLT CREW HAS PRESSURIZATION PROBS; DSNDS AND AVOIDS TCAS DEPICTED TRAFFIC.

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MY FO HAD APPARENTLY TURNED THE AUX HEAT SWITCH ON IN ERROR WHEN ATTEMPTING TO TURN ON THE AIR CONDITIONER. I ASKED MY FO TO TURN OFF THE COCKPIT AUX HEATER; AS IT WAS CERTAINLY NOT NECESSARY. HE APPARENTLY MISTAKENLY TURNED OFF THE 'CABIN AIR' SWITCH RATHER THAN THE COCKPIT AUX HEATER. IN LEAR JETS; THE 'CABIN AIR' SWITCH IS THE MASTER CTL SWITCH FOR THE PRESSURIZATION SYS. UNDER NORMAL CONDITIONS; IT ALLOWS ENG BLEED AIR INTO THE PRESSURIZATION SYS TO CTL THE CABIN PRESSURE OF THE ACFT IN NORMAL OP. WITH THE CABIN AIR SWITCH 'OFF;' ENG BLEED AIR IS NOT ALLOWED TO PRESSURIZE THE CABIN AND NORMAL PRESSURIZATION IS LOST. THE RESULT OF THE FO'S INADVERTENT DEACTIVATION OF THE 'CABIN AIR' SYS WAS TO DEPRESSURIZE OUR CABIN. THE OUTFLOW VALVES WOULD CLOSE TO TRY TO CONTAIN THE EXISTING PRESSURE BUT THIS WOULD BE; AND WAS; ONLY A TEMPORARY FIX. AS NO NEW BLEED AIR WAS ALLOWED TO PRESSURIZE THE ACFT; PRESSURIZATION GRADUALLY LEAKED OUT AND OUR CABIN ALT ROSE TO ABOVE 10000 FT. ABOVE 10000 FT A NUMBER OF THINGS OCCUR. FIRST A CABIN ALT WARNING SOUNDS (AND ILLUMINATES A CAUTION ADVISORY) AND SUBSEQUENTLY THE PRESSURIZATION SYS ATTEMPTS TO CTL THE CABIN ALT BY SWITCHING INTO AN EMER MODE. IN THIS MODE; THE BLEED VALVES TRIP OPEN AND HOT; UNMODULATED; HIGH PRESSURE AIR IS PUMPED DIRECTLY INTO THE CABIN. THIS STOPS PRESSURE LOSS; BUT IS VERY NOISY AND QUITE HOT. THE PREVIOUSLY MENTIONED AURAL WARNING (UNSILENCEABLE) WAS ALSO CONTINUING TO SOUND MAKING COMS VIRTUALLY IMPOSSIBLE. (THE COMBINATION OF AURAL WARNING AND HIGH PRESSURE AIR RUSHING INTO THE COCKPIT IS DEAFENING.) AT THIS POINT; I ELECTED TO BEGIN A DSCNT IN COMPLIANCE WITH THE ASSOCIATED EMER PROC. I ADVISED ATC THAT WE WERE EXPERIENCING PRESSURIZATION PROBS AND NEEDED TO DSND TO BELOW 10000 FT. DUE TO THE NOISE IN THE COCKPIT; I WAS UNABLE TO HEAR ATC'S RESPONSE. WE HAD ONLY DSNDED A FEW FT WHEN I NOTICED A TCAS TARGET IN FRONT OF AND BELOW OUR ACFT. I OBTAINED A VISUAL ON THE TFC (A B757) WHICH WAS XING R TO L AND BELOW OUR ACFT. I IMMEDIATELY LEVELED OFF AND TURNED SLIGHTLY TO THE R TO INCREASE THE OFFSET. OUR TCAS ONLY SHOWED THE POS AND ALT OF THE B757 AND ITS STATUS NEVER ELEVATED TO AN ALERT OR RA. AFTER THE B757 WAS WELL CLR TO OUR L; I CONTINUED THE DSCNT TO 8500 FT WHERE I WAS ABLE TO RESET THE EMER AIR TRIP AND REGAIN CTL OF THE ACFT PRESSURIZATION. WITH OUR COMS WITH ATC RESTORED; WE CONTINUED WITH NO FURTHER EVENT.