ATX FLEW WRONG HEADING ON DEP; HAD ACFT EQUIPMENT PROBLEMS AND OVERSHOT ALT ON CLIMB CREATING LESS THAN STANDARD SEPARATION WITH ANOTHER SMT.

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ACCORDING TO THE FIR CLRNC THAT I READ BACK TO PONTIAC CLRNC DELIVERY (AND RECEIVED A 'READBACK CORRECT'); I WAS TO CLB TO 3000' ON THE RWY HDG (270 DEGS) AND EXPECT RADAR VECTORS TO THE PONTIAC 007 DEG R TO INTERCEPT THE LONDON 270 DEG R TO LONDON VOR (YXU). FROM THE TWR CHIEF AT PONTIAC TWR; I LATER LEARNED FROM THE TAPE PLAYBACK; I WAS ISSUED THE 077 DEG R. HOWEVER; I WROTE DOWN AND READ BACK THE 007 DEG R. AND ALTHOUGH LATER COMS WITH THE TWR MENTIONED THE 077 DEG R AGAIN; I WAS CONCENTRATING ON GETTING THE PROPER ALTS TO FLY AND KNEW THAT THE ROUTING WAS AS I HAD ALREADY WRITTEN DOWN. AFTER TKOF ON RWY 27; I CLBED ON THE RWY HDG TO 3000'. WHEN I WAS TURNED OVER TO DEP CTL (124.9) I WAS FURTHER CLRED TO 5000' AND WAS TOLD TO TURN TO A HDG OF 060 DEGS. AS I BEGAN THE CLBING TURN; I ENTERED THE SOLID OVCST. I WAS EXPERIENCING SOME CONFUSION OVER THE HDG (060 DEGS) AND HOW IT WOULD GET ME TO WHAT I THOUGHT WAS SUPPOSED TO BE THE 007 DEG R. AT THIS POINT; I NOTICED THE HDG FLAG WAS SHOWING ON MY HSI AND HAD THE ADDED PROB OF NOT KNOWING IF I WAS GETTING THE CORRECT HDG INFO. AT THE SAME TIME I NOTICED THAT ICE WAS BEGINNING TO FORM ON THE WINDSHIELD AND FELT I SHOULD DOUBLECHK TO SEE THAT THE PROPER ICING EQUIP WAS INDEED ON. AT THIS POINT I RETARDED THE PWR LEVERS SOMEWHAT TO SLOW MY SPD AND RATE OF CLB. WHILE I WAS DEALING WITH THIS EMER SITUATION; DET DEP CALLED AND ASKED ME TO CHK MY ALT. I FIRST LOOKED AT MY ALTIMETER AND SAW THAT IT INDICATED 5800'. THIS WAS WELL ABOVE MY ASSIGNED 5000' ALT AND I BEGAN AN IMMEDIATE DSCNT TO 5000'. I DID NOTICE THAT I HAD CORRECTLY SET 5000' ON THE ALT ALERTER AND THAT I HAD THE CORRECT SETTING ON MY ALTIMETER. THE NEXT XMISSION FROM DET WARNED ME OF SMT Y TFC AT 12 O'CLOCK AND 6000'. I HAD JUST CLRED THE TOP OF THE CLOUD DECK AS I STARTED MY DSCNT; AND IN THE SHORT SECS THAT I WAS CLR OF THE CLOUDS COULD NOT SPOT THE TFC. MY ALT ALERTED FAILED TO WORK; AND IN THE CONFUSION; WAS AN ADDED FACTOR THAT HELPED TO CAUSE THE DEVIATION. ON RETURN TO MY HOME BASE; I HAD THE EQUIP CHKED AND IT WAS FOUND TO BE INOP. I FEEL THAT I DID MY BEST IN DEALING WITH AN EMER SITUATION THAT WAS CAUSED BY INITIAL CONFUSION OVER MY CLRNC AND A DOUBLE EQUIP FAILURE IN SOLID IFR CONDITIONS.