A B350 DEVELOPED A BLEED AIR FAULT AFTER TKOF IMC. THE SOLO PILOT DID NOT FOLLOW HIS CLEARED ROUTING AS HE WORKED THE SYSTEM PROBLEM.

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THE WX AT ZZZ1 AND ZZZ2 HAD CAUSED THE CANCELLATION OF MOST FLTS DUE TO ICE AND SNOW. ONE OF OUR BEST CHARTER CUSTOMERS WAS TRYING TO GET TO ZZZ3 FOR AN IMPORTANT MEETING AND HAD HIS FLT CANCELED. HE CALLED AND ASKED IF WE COULD GET HIM AND AN ASSOCIATE TO ZZZ2. THE WX HAD PASSED N OF OUR ARPT WHICH AT THE TIME WAS GOOD VFR; ALTHOUGH THEY WERE HAVING FREEZING RAIN AT ZZZ1. I CHKED THE WX AND ADVISED HIM THAT IF THEY COULD DEPART FROM OUR ARPT WITHIN THE NEXT FEW HRS; WE COULD GET THEM TO THEIR DEST. THEY ARRIVED EARLIER THAN I HAD EXPECTED; BUT IT WAS ALREADY STARTING TO SNOW. I HAD THE LINE CREW LEAVE THE ACFT INSIDE THE HANGAR TO KEEP IT CLEAN OF ICE AND SNOW. I HAD THE PAX LOAD IN THE HANGAR AND GAVE THE PAX BRIEFING AND WENT THROUGH THE PRE-START CHKLIST BEFORE I HAD THE LINE CREW TOW THE ACFT OUT. AFTER A NORMAL START; I STARTED TO TAXI TO THE ACTIVE RWY. AS THE TXWYS HAD SOME ACCUMULATION OF SLUSH; I TURNED ON THE BRAKE DEICE SYS TO KEEP THE BRAKES FROM FREEZING UP. I TRIED TO GET MY CLRNC THROUGH THE FSS BY USING THEIR REMOTE FREQ ON MY COM #1. WE HAD TROUBLE HEARING EACH OTHER; SO I SWITCHED TO COM #2 WHICH HAS A HIGHER ANTENNA LOCATION. RECEPTION WAS BETTER AND I COPIED MY IFR CLRNC. I SET UP COM #1 FOR THE DEP FREQ AND TUNED COM #2 TO THE UNICOM FREQ. THE ARPT PERSONNEL WERE PLOWING THE RWYS AND WERE CURRENTLY ON THE ONE I WAS WAITING TO DEPART ON. I COMPLETED MY FINAL CHKS AND SET THE HDG BUG ON THE HSI TO RWY HDG. THE PLOW EXITED THE RWY AND WE DEPARTED JUST AS A HEAVIER SNOW SHOWER WAS MOVING IN AND REDUCING VISIBILITY TO OUR LEGAL TKOF MINIMUM. AFTER DEP; I LET THE WHEELS SPIN DOWN TO THROW OFF SOME OF THE SLUSH AND RETRACTED THEM. I STARTED A L TURN AND NOTICED THAT THE L BRAKE DEICE LIGHT WAS STILL ON. I RECYCLED THE SWITCH; BUT THE L BRAKE BLEED AIR VALVE APPEARED TO BE STUCK ON. I LEVELED THE ACFT AND TURNED ON THE AUTOPLT TO FLY THE ACFT WHILE I WAS DISTR TRYING TO GET THE VALVE TO CLOSE. I CYCLED THE BRAKE DEICE SWITCH AGAIN AND ALSO THE L BLEED AIR VALVE. THE VALVE HAD FAILED OPEN. WITH THE WHEELS IN THE WELLS; IT WOULD ONLY BE MINS BEFORE I GOT A RED L BLEED AIR FAIL LIGHT AND MASTER WARNING. I TRIED TO CONTACT DEP TO SEE IF I COULD GET VECTORS BACK TO THE ARPT FOR AN APCH. I WANTED TO SWITCH TO ANOTHER ACFT AND TRY AGAIN. I COULD HEAR OTHER ACFT; BUT NOT ATC. I TURNED OFF THE L BLEED AIR SYS; WHICH WOULD HAVE BEEN THE MEMORY ITEM WHEN THE L BLEED AIR FAIL LIGHT CAME ON. I TRIED SEVERAL TIMES TO REACH ATC ON BOTH COM RADIOS WITH THE SAME RESULTS. I LOOKED AT MY CLRNC NOTE AND NOTICED '280' AND I WAS FLYING WBOUND; SO I TURNED MY HDG BUG TO 280 DEGS. A SHORT WHILE LATER I LOOKED AT MY CLRNC AGAIN AND REALIZED THAT '280' WAS MY EXPECTED FINAL FLT LEVEL. MY HDG SHOULD HAVE BEEN 180 DEGS AND I TURNED S. AFTER MANY FAILED ATTEMPTS TO REACH DEP; I TUNED IN CTR AND HAD NO PROB TALKING WITH THEM OR ANYONE ELSE DURING THE REMAINDER OF THE FLT. WHILE THE CTR CTLR WAS COORDINATING MY FLT; HE GAVE ME THE ALTIMETER SETTING. IT WAS WELL OFF OF WHAT I HAD SET; AND ALTHOUGH THE AUTOPLT WAS LOCKED ON 3000 FT; I WAS ACTUALLY MUCH HIGHER. I DON'T KNOW IF I SET IT WRONG; ACCIDENTALLY CHANGED IT; OR MISSED SETTING IT IN MY HASTE. BY THIS TIME I WAS ON MY WAY TO ZZZ3; SO I CONTINUED. THE REST OF THE FLT WAS UNEVENTFUL AND I HAD A MAINT SHOP AT ZZZ3 MEL THE BRAKE DEICE VALVE AND I HAD IT REPLACED THE NEXT DAY. CONTRIBUTING FACTORS WERE RUSHING DUE TO A POP-UP TRIP; TRYING TO BEAT THE WX TO MAKE TKOF MINIMUMS; RUSHING TO KEEP A 'CLEAN' (NOT CONTAMINATED BY SNOW) ACFT; CONFUSION OVER MY OWN CLRNC NOTE (ALTHOUGH I DID WRITE 'H180' FOR THE HDG); NOT DOUBLECHKING THE ALTIMETER SETTING; COM PROBS WITH ATC; AND A SMALL MECHANICAL PROB RIGHT AFTER TKOF THAT I WAS TRYING TO PREVENT FROM BECOMING A RED LIGHT EMER CHKLIST PROB. MOST OF MY FLYING HAS BEEN SINGLE PLT; EVEN IN ACFT THAT REQUIRE A TYPE RATING (THROUGH THE COMMUTER CLASS OR AN EXEMPTION). I AM VERY COMFORTABLE IN THAT ROLE; AND HAVE HAD MORE INCIDENTS OF ERRORS AS A CREW THANAS A SINGLE PLT. THIS TIME THOUGH; IT WOULD HAVE BEEN A HELP TO HAVE SOMEONE ELSE TO DEAL WITH THE PROB WHILE I FLEW THE ACFT; OR AT LEAST SOMEONE ELSE TO POINT OUT MY HDG AND ALTIMETER MISTAKES. I NOTICED THE HDG AND ALT IRREGULARITIES ON MY OWN; BUT ATC MAY HAVE TRIED TO POINT THEM OUT; I JUST NEVER HEARD DEP. CTR DID NOT COMMENT ON EITHER. BOTH LASTED ONLY MINS AND I DO NOT BELIEVE ANY OTHER TFC WAS INVOLVED. I NEVER SAW ANOTHER ACFT ON MY TCASII DURING THAT TIME; BUT I WAS ONLY INCLUDING THE TCAS IN MY REGULAR SCAN AND NOT WATCHING IT. TRACON DID CALL THE ARPT OFFICE RIGHT AFTER I DEPARTED AND ASKED IF THEY COULD TRY TO CONTACT ME. THEY COULD NOT BECAUSE MY CELL PHONE WAS OFF AND I HAD BOTH RADIOS TUNED TO DEP. BRAKE DEICE VALVES ARE NOTORIOUS FOR STICKING. I NEED TO FLY THE PLANE FIRST; THEN SOLVE THE PROB. COM TROUBLES DIDN'T HELP.