A CE560 CREW WITH AIR CONDITIONING AND RADIO PROBLEMS MISSED AN LAS SID HDG AND BEGAN A CLB WHEN TOLD TO REMAIN LEVEL ONLY TO GET A TA.

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WE DEPARTED LAS ON RWY 19R VIA THE SHEAD 5 DEP. DURING THE TURN AT JAKER; THE CTLR ADVISED THAT HE THOUGHT WE HAD MISSED THE TURN AND ASSIGNED A HDG OF 220 DEGS. AT A POINT W OF THE ROPPR-MDDOG SEGMENT; WE WERE ASSIGNED 250 DEGS ON THE HDG; 250 KTS ON THE AIRSPD; AND 11000 FT MSL. A FEW MINS LATER; THE CTLR INSTRUCTED US TO PROCEED DIRECT TO SHEAD. WE QUESTIONED THE CTLR AS TO WHETHER WE SHOULD RESUME THE DEP AT SHEAD AND HE SAID 'YES.' THE CAPT DIALED IN 14000 FT MSL AND I INITIATED A CLB. AT 11700 FT; WE RECEIVED A TFC ALERT FROM TCAS AND DEP SIMULTANEOUSLY. DEP INSTRUCTED US TO TURN TO A HDG OF 320 DEGS AND DSND TO 11000 FT MSL. WE WERE THEN ADVISED OF A PLTDEV BY DEP AND GIVEN A PHONE NUMBER TO CALL. THE FLT DIVERTED DUE TO FAULTY ENVIRONMENTAL AND RADIO SYS. ON THE GND AT LAS WE EXPERIENCED SOME RADIO TROUBLE. WE CONCLUDED THAT SINCE THE #2 RADIO IS OUR PRIMARY RADIO AND ITS ANTENNA IS LOCATED ON THE BOTTOM OF THE ACFT; THAT WAS THE REASON WE HAD TROUBLE COMMUNICATING WITH THE TWR. THE #1 RADIO; WHOSE ANTENNA IS ON TOP OF THE ACFT; SEEMED TO WORK PROPERLY. HOWEVER; ONCE ENRTE; WE EXPERIENCED INTERMITTENT TROUBLE WITH OUR RADIOS. THE AIR CONDITIONING SYS WAS INOP. AS WE INITIATED THE TKOF ROLL; THE AIRFLOW IN THE CABIN BECAME VERY LOUD. IT SEEMED AS THOUGH AN OUTFLOW VALVE IN THE PRESSURIZATION SYS WAS OPEN. ONCE IN THE AIR; THE LOUD AIRFLOW NOISE SUBSIDED. HOWEVER; THE TEMP IN THE FLT DECK WAS EXTREMELY WARM; ESPECIALLY AT FL380. INDICATIONS OF THE EXTREME TEMP INCLUDED: 1) YOKE WAS TOO WARM TO TOUCH WITH BARE HAND. 2) BAR OF SOAP IN MY BAG IN THE CABIN MELTED. 3) POP CANS IN THE CABIN CHANGED SHAPE. IN CONCLUSION; THE ENVIRONMENTAL AND COM PROBS WE WERE EXPERIENCING MAY HAVE CONTRIBUTED TO MISCOM BTWN US AND LAS DEP. HOWEVER; WHEN THE CTLR CLRED US DIRECT TO SHEAD AND TO RESUME THE SHEAD 5 DEP; WE UNDERSTOOD THAT TO MEAN WE SHOULD BE AT 14000 FT MSL BY THE TIME WE REACHED SHEAD.