M20P PLT DEPARTS 7D2 ON WRONG HDG; CALLING DTW AT DEST TO RESOLVE CLRNC AND FLT ISSUES.

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I OBTAINED WX BRIEFING FSS APPROX XA30 AND FILED AN IFR FLT PLAN. INTENDED RTE OF FLT 7D2 DIRECT HADAR INTXN DIRECT DOLFN INTXN DIRECT ERI DIRECT TDT DIRECT PSB TO ONV (LNDG). I CONTACTED DETROIT APCH VIA REMOTE COMS ON 121.725 FOR A CLRNC. UPON CONTACT; CTLR MADE SEVERAL ATTEMPTS TO PROVIDE CLRNC; BUT WAS INDISCERNIBLE TO ME. MY CLRNC WAS AS FILED; EXCEPT TO TYCOB RATHER THAN HADAR AS FIRST WAYPOINT. I ASKED SEVERAL TIMES FOR CLARIFICATION WITH WHAT SOUNDED LIKE 'COB INTXN.' AFTER SEVERAL TRIES; HE SPELLED 'T-Y-C-O-B.' AT THIS POINT I UNDERSTOOD THE CLRNC AS FOLLOWS: 7D2 CLRED TO UNV AS FOLLOWS: FOLLOWING DEP PROCS DIRECT TYCOB DIRECT DOLFN DIRECT ERI DIRECT TDT DIRECT PSB DIRECT UNV. FOLLOWING CLRNC; I ADJUSTED RNAV FROM HADAR TO TYCOB (THINKING MY SETTINGS WERE OK). WITH 3 MIN VOID TIME; I SET MY RADIOS FOR TKOF. UPON DEPARTING 7D2 FROM RWY 27; I PROCEEDED XWIND FOR DOWNWIND EXPECTING TO DEPART ARPT ON THE DOWNWIND AT 090 DEG HDG. ABOUT THAT TIME DTW APCH ASSIGNED 190 DEGS; CLB AND MAINT 5000 FT (SO I UNDERSTOOD). I PROCEEDED ON 190 DEG HDG. (AT THIS TIME I NOTICED MY AMMETER NEEDLE FLUCTUATING AND I WAS CONCERNED ABOUT LOSS OF PWR AND COM.) DTW APCH ASKED TO CONFIRM 090 DEG HDG AND I RESPONDED WITH 'PROCEEDING 090 DEGS FROM 190 DEGS' (AS I INDICATED; UNDERSTOOD 190 DEGS). UPON APCHING 5000 FT; DTW APCH CLRED DIRECT TO TYCOB. I RESPONDED AND PUNCHED IN RNAV (TYCOB INTXN). DTW APCH ASKED TO VERIFY DIRECT TYCOB. I CONFIRMED 125 DEG HDG. DTW SUGGESTED 140 DEGS. (AT THIS TIME I NOTICED THE FREQ TO YQG WAS IN AT 113.6 INSTEAD OF 113.8 FOR RNAV WAYPOINT NAV.) I INFORMED DTW THAT I HAD RE-ESTABLISHED THE CORRECT NAV SIGNAL AND WAS CORRECTING. DURING FLT; I WAS ASKED TO CALL DTW. I COMPLIED WITH REQUEST SHORTLY AFTER LNDG AT UNV. DTW NOTICED SEVERAL ATTEMPTS AT TYCOB. I EXPLAINED THE CTLR WAS NOT UNDERSTANDABLE. (IT COULD HAVE BEEN MY RADIOS WERE NOT WORKING PROPERLY. JUST STARTED UP ACFT AND INSTS WERE COLD -- OUTSIDE AIR TEMP AT ZERO DEGS.) WAS FURTHER ASKED WHY I DEPARTED 7D2 ON XWIND TO A 190 DEG HDG. I INFORMED I UNDERSTOOD A HDG OF 190 DEGS AND NOT 090 DEGS BY THE CTLR. WAS FURTHER ASKED WHY I COULD NOT COMPLY WITH NAV DIRECT TO TYCOB. I INFORMED OF MY SET-UP PROB (YQG; NOT ON 113.8). FOLLOWING MY OBSERVATION I CORRECTED. PROBS: 1) WX CONDITIONS IMPACTED RADIO'S PERFORMANCE. 2) MANUAL ERROR IN SETTING UP NAV RADIOS. 3) ACCEPTING 3 MIN CLRNC WINDOW AND NOT CHKING INSTS. 4) NOT QUESTIONING 190 DEG HDG IN LIEU OF DOWNWIND DEP PROC. CORRECTIVE ACTIONS: 1) ALLOW MORE TIME TO WARM UP INSTS ON COLD DAY. 2) QUESTION RELEASE WINDOW WHEN NOT POSITIVE OF INST SETTINGS. 3) COMPLETE PROC DEP AND QUESTION DIRECTIONS IN DIFFERENCE. 4) DOUBLECHK INSTS PRIOR TO USING WAYPOINTS. OTHER FACTORS: 1) CLR VFR DAY WITH UNLIMITED VISIBILITY IN ALL DIRECTIONS. NO VISIBLE TFC. 2) DID NOT DELIBERATELY DEVIATE FROM FLT PLAN AND ACCEPTED DTW CLRNC.