OPDEV OCCURRED WHEN AN IFR C172 ENTERS BDL AIRSPACE WITHOUT COORD OR HDOF BY RPTR. THE C172 WAS NOT RADAR IDENTED BY THE RPTR AND WAS INITIALLY TREATED AS A VFR ACFT.

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ACFT #1 WAS RELEASED FOR DEP IFR FROM PSF TO BDL. UNFORTUNATELY ACFT #1 CHKED ON WITH ME DURING A PERIOD OF MANY VFR ACFT (MANY WITH POOR RADIOS); IFR INBOUNDS; AND SATELLITE OPS. I WAS WORKING BOTH E FEEDER AND FINAL VECTOR COMBINED. DUE TO OUTSIDE NOISE; CONDUCTING A RELIEF BRIEFING; AND MANY OTHER DISTRS (BAD RADIOS; MANUAL HDOFS FROM BDL; CONSCIOUS AND SUBCONSCIOUS COMPLIANCE WITH TFC COUNT PROCS; ETC); I INADVERTENTLY ISSUED THE ALB ALSTG TO ACFT #1 THINKING THAT HE WAS A SIMILAR VFR ACFT CHKING WITH ME 'LEVELING' AT AN ALT (HE CALLED 'LEAVING' AN ALT). HE ALSO HAD A BAD RADIO AND DID NOT RPT AS 'DEPARTING PSF.' AFTER HEARING THE ALB ALSTG; ACFT #1 REQUESTED DIRECT CTR BUT WAS UNHEARD BY ME AND NOT ACKNOWLEDGED. I CONTINUED OTHER ATC DUTIES AND INSTRUCTION WHILE CONDUCTING A RELIEF BRIEFING. WITHIN MINS OF ACFT #1 DEPARTING PSF I WAS RELIEVED FROM THE POS -- ANY CHANCE OF CATCHING THE MISTAKE GONE. DURING THE RELIEF BRIEFING; I BRIEFED THAT ACFT #1 WAS STILL EXPECTED TO DEPART FROM PSF. ACFT #1 NEVER CALLED AGAIN UNTIL OUTSIDE OF ALB AIRSPACE. HE WAS NEVER GIVEN 'RADAR CONTACT;' NEVER CHKED LEVEL AT 5000 FT; AND NEVER RPTED ANY FIXES OR NAVAIDS. HIS XPONDER WAS EITHER INOP; WRONG CODE; INTERMITTENT; OR ALL OF THE ABOVE. NEVERTHELESS; THE ACFT XPONDER AND TARGET WAS NEVER SEEN BY ATC. I EXPECTED ACFT #1 TO DEPART PSF DIRECT DXT DIRECT STELA V130 BDL. HE WAS TO BE ISSUED A FULL RTE CLRNC BUT ACTUALLY WAS READ AN 'AS FILED' CLRNC FROM RADAR DATA WHICH DELETED MUCH OF THE RTE. NUMEROUS FACTORS WERE INVOLVED IN THIS SIT; FROM BAD RADIOS; TO INEXPERIENCED PLTS (PLT WAS RATED FOR 5 DAYS). FROM BAD TIMING ON POS RELIEF; TO EQUIP FAILURE. ALMOST ANY SINGLE ONE OF THESE FACTORS NOT HAPPENING MAY HAVE PREVENTED ACFT #1 FROM VIOLATING BDL AIRSPACE.