INSTRUCTOR WITH SPI REQUESTING TO TRANSIT TCA HAS INOP XPONDER. CONTINUES AND ENTERS ATA WITHOUT CLRNC.

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THIS TRAINING FLT OBJECTIVE WAS TO FLY VFR FROM LIVERMORE MUNICIPAL ARPT TO HALF MOON BAY ARPT AND SUBSEQUENTLY PRACTICE REPEATED TOUCH-AND-GO'S. AT HALF MOON BAY; MY INTENTION WAS TO REQUEST A TCA CLRNC FROM BAY APCH CTL (TRACON). ONCE WE LEVELED OFF AT 2500 FT MSL; WBOUND FROM LIVERMORE; I CALLED BAY APCH AND GAVE THEM MY REQUEST. IT WAS AT THIS TIME WE MUTUALLY DISCOVERED THAT MY XPONDER WAS NOT WORKING AT ALL. AT THIS POINT BAY APCH INSTRUCTED ME TO PROCEED TO HALF MOON BAY VFR AND TO REMAIN CLR OF THE TCA. I HAD TO MAKE A VERY RAPID DECISION AS I WAS NOT COMFORTABLE WITH FLYING IN THAT AIRSPACE WITHOUT A XPONDER AND YET I HAD FLOWN IN AND AROUND THIS AIRSPACE MOST OF MY CAREER AND FELT I HAD ENOUGH EXPERIENCE TO BE ABLE TO NAV AROUND THE COMPLEX WEB OF TCA; ARSA'S; AND ATA'S ALONG THE RTE. BUT I ALSO FELT SOMEWHAT; THOUGH NOT CONVINCINGLY ENOUGH; TURN BACK AND GO EBOUND WHERE THE AIRSPACE WAS LESS COMPLEX AND LESS CONGESTED. THE XPONDER INOP AND SUDDEN INDECISION BECAME A DISTR. ALSO THE STUDENT I WAS WORKING WITH ON THAT AFTERNOON WAS NEW TO TRAVELING TO THE W OF LIVERMORE OVER SAN FRANCISCO BAY AND I WAS VERY DISTRACTED AT HAVING TO ASSIGN HIM A SERIES OF HDGS AND ALTS; WHILE I HANDLED RADIOS; IN ORDER TO STAY LEGAL. I ALSO BECAME CONFUSED BECAUSE AFTER BAY APCH TOLD ME THEY COULD NOT HELP ME BECAUSE OF MY INOP XPONDER; I NEVER HEARD 'FREQ CHANGE APPROVED.' MY REACTION SHOULD HAVE BEEN TO QUERY ATC OR REQUEST FREQ CHANGE ON MY OWN TO GET A BETTER IDEA OF WHAT THEY WANTED ME TO DO. I SHOULD HAVE KNOWN TO CHANGE FREQS RIGHT AWAY. ALSO; I HAD COMMITTED A NAV ERROR AS I HAD INTENDED TO FOLLOW THE SAN MATEO BRIDGE AS A NAVIGATIONAL LANDMARK GOING WBOUND BUT SUDDENLY DISCOVERED I WAS FOLLOWING THE DUMBARTON BRIDGE. ALL OF THESE FACTORS HAD ME RATHER CONFUSED AND DISTRACTED AND BY THE TIME I DECIDED ON A COURSE OF ACTION AND FOUND MY POS; I DISCOVERED I WAS APPROX 2-3 NM FROM THE PALO ALTO ARPT AT 1300 FT MSL. WHEN I CAME TO THIS REALIZATION; I WAS NW OF THE ARPT HDG TOWARDS HALF MOON BAY. IN OTHER WORDS; I WAS 1-2 MI FROM LEAVING ITS ATA AND MY NEXT CONCERN WAS CLBING OVER THE HILLS AND CONTACTING HALF MOON BAY TFC ASAP SO I DECIDED AT THAT TIME NOT TO CALL PALO ALTO TWR. ON MY RETURN TRIP TO LIVERMORE; I CALLED BAY APCH TO INFORM THEM OF MY PROB AND THIS TIME CALLED PALO ALTO AND HAYWARD TWRS FOR ATA TRANSITION CLRNCS AS I SHOULD HAVE DONE THE FIRST TIME AROUND.