UNABLE TO CONTACT MIA DEP ON THE GND AT HWO; FLT CREW OF C550 TOOK OFF INTO PRESIDENTIAL TFR.

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OUR FLT WAS SCHEDULED ON OCT/FRI/04 AT APPROX XA30 DEPARTING TO EWY. THE PIC FILED THE IFR FLT PLAN WITH FSS. THE CTL TWR AT HWO WAS CLOSED AT OUR DEP TIME. WE UNSUCCESSFULLY ATTEMPTED TO CONTACT MIA DEP. WHILE ON THE GND TO ACTIVATE THE IFR FLT PLAN; THE PIC MADE THE DECISION TO DEPART VFR. ONCE AIRBORNE; IMMEDIATELY TURNED N; SQUAWKED 1200; CLBED TO 1200 FT MSL AND ACTIVATE THE IFR FLT PLAN WITH MIA DEP. AT 500 FT MSL WE ATTEMPTED TO CONTACT MIA DEP. I COULD HEAR MIA BUT THEY DID NOT ANSWER MY MULTIPLE RADIO CALLS. I THEN ATTEMPTED TO CONTACT BOTH MIA AND FLL ON NUMEROUS FREQS. CONTINUING TO TRY DIFFERENT FREQS; AGAIN I COULD HEAR XMISSIONS; BUT THEY DID NOT RESPOND TO MY XMISSIONS. ULTIMATELY MIA APCH REPLIED TO OUR XMISSIONS AND ASSIGNED A XPONDER CODE IDENTING OUR ACFT 20 NM W OF HWO AT 2500 FT MSL. MIA THEN ACTIVATED OUR FILED IFR FLT PLAN TO KEY WEST. THEN MIA ASKED FOR PIC'S NAME AND REQUESTED THE PIC CONTACT MIA VIA TELEPHONE UPON LNDG IN KEY WEST. WE HAD ENTERED THE PRESIDENTIAL TFR WITHOUT A CLRNC. WE LANDED AT EWY UNEVENTFULLY.