INSTRUCTOR WITH INST STUDENT HAD VACUUM PUMP FAILURE IN IMC. UNABLE TO COMPLY WITH ALTS AND VECTORS ISSUED.

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I DEPARTED BARNSTABLE MUNICIPAL ARPT ON AN IFR FLT PLAN WHICH WOULD TAKE MYSELF AND MY INST STUDENT TO NANTUCKET; MA; ON AN INST TRAINING FLT. WE DEPARTED RWY 15; WE PENETRATED THE OVCST AT 500-600 FT; AND WERE PROMPTLY INSTRUCTED BY HYANNIS TWR TO CONTACT CAPE APCH. I CHANGED FREQS AND CONTACTED APCH CTL. I BRIEFLY TOOK MY EYES OFF OF THE INSTS; AS I FELT CONFIDENT IN MY STUDENT'S ABILITY TO KEEP THE AIRPLANE UNDER CTL BY REF TO INSTS. I RETURNED MY EYES BACK TO THE INST PANEL. I NOTICED THAT THE ATTITUDE INDICATOR WAS SHOWING THE ACFT TO BE IN A FAIRLY STEEP DSNDING BANK TO THE R. I BEGAN TO TELL MY STUDENT TO CORRECT FOR THIS. HE SAID 'SOMETHING'S WRONG.' AFTER XCHKING THE INSTS; I COULD SEE THAT IN FACT WE WERE IN A CLBING L BANK. I HESITATED FOR A BRIEF MOMENT; REFUSING TO BELIEVE MY INSTS; THEN IMMEDIATELY ASSUMED A VACUUM FAILURE. TAKING CTL OF THE AIRPLANE I BEGAN TO LEVEL THE WINGS; AND DECREASE OUR PITCH; AS I COULD SEE OUR AIRSPD DECREASING. I CONTACTED CAPE APCH AND ADVISED THEM OF OUR SIT; REQUESTING VECTORS FOR AN IMMEDIATE RETURN TO HYANNIS. THEY RESPONDED AND ASKED IF I WISHED TO DECLARE AN EMER; TO WHICH I ANSWERED 'NEGATIVE;' FEARING THE POSSIBLE PAPERWORK AND QUESTIONS TO ANSWER IF I DID SO. I LEVELED OFF AT MY ASSIGNED ALT OF 1700 FT AND WAS SO FOCUSED ON TRYING TO CTL THE AIRPLANE WITH NO ATTITUDE INDICATOR; THAT I FAILED TO REALIZE THAT THE AIRPLANE HAD DEVIATED TO THE N; FROM OUR INITIALLY ASSIGNED HDG OF 150 DEGS. SHORTLY THEREAFTER; CAPE APCH INSTRUCTED ME TO MAKE A CLBING R TURN TO 3000 FT AND A HDG OF 200 DEGS. AS I BEGAN FIGURING OUT THE AMOUNT OF TIME TO TURN USING A TIMED TURN AT A STANDARD RATE; APCH CALLED BACK AGAIN WITH THE SAME INSTRUCTION; AND A SENSE OF URGENCY. I DID MY BEST TO COMPLETE AN ACCURATE TIMED TURN; WHILE CLBING; BUT THE SENSE OF URGENCY AT HAND FORCED ME TO COUNT TOO QUICKLY; RESULTING IN AN EARLY ROLLOUT AND FAILURE TO COMPLY WITH THE VECTOR IN A TIMELY MANNER. I LEVELED OUT AT 3000 FT AND NOTICED THAT THE HDG INDICATOR AND MAGNETIC COMPASS SHOWED THE SAME HDG; AND THE ATTITUDE INDICATOR SEEMED TO BE WORKING. HOWEVER; I DECIDED THAT I WOULD NOT TRUST THEM AND WOULD KEEP THEM OUT OF MY SCAN; USING ONLY MY REMAINING INSTS; AND USING TIMED TURNS IN ORDER TO COMPLY WITH VECTOR HDGS. CAPT APCH CALLED BACK; AND THE CTLR GAVE ME A TELEPHONE NUMBER TO CALL WHEN I LANDED; AND INSTRUCTED ME TO ASK FOR THE SHIFT SUPVR. I BEGAN TO FEEL ADDED TENSION IN AN ALREADY TENSE SIT; AS I BELIEVED THAT THIS MEANT I WOULD BE IN SOME SORT OF TROUBLE. I WAS THEN GIVEN SEVERAL VECTORS; WITH WHICH I TRIED MY BEST TO COMPLY USING TIMED TURNS; AND A MAGNETIC COMPASS; BUT HAD LIMITED SUCCESS; DEVIATING FROM MOST OF THEM DUE TO THE ADDED TENSION WHICH I FELT. I WAS THEN TOLD TO DSND TO 1700 FT AND EXPECT AN ILS APCH TO HYANNIS. FOCUSING MAINLY ON TRYING TO CTL THE AIRPLANE; AND MAINTAINING MY HDG USING ONLY A MAGNETIC COMPASS; I DSNDED TO APPROX 1200 FT BEFORE BEING TOLD BY THE CTLR THAT I WAS TOO LOW AND HAD TO CLB BACK UP TO 1700 FT. APCH CTL; SHORTLY THEREAFTER; CALLED BACK AND ASKED IF I WAS RECEIVING THE LOC. I LOOKED TO SEE IF I WAS; AND ALL I SAW IN BOTH WINDOWS WERE 'NAV' FLAGS. I RESPONDED THAT I WAS NOT RECEIVING THE LOC; AND AFTER SEVERAL EXCHANGES WITH ATC I REALIZED THAT THEY WERE GIVING ME THE ILS 24 APCH; AND I WAS EXPECTING THE ILS 25 APCH; FOR WHICH I WAS ALREADY SET UP. I QUICKLY LOOKED UP THE ILS 24 APCH PLATE; AND MANAGED TO GET THE CORRECT FREQS FOR THE APCH AND GET SET UP. I WAS VECTORED BACK TO THE 24 LOC; AND THE NEEDLE BEGAN TO COME IN SHORTLY THEREAFTER. CAPE APCH THEN CLRED ME FOR THE APCH; ADVISING ME THAT I WAS 2 MI FROM THE OM. SHORTLY THEREAFTER; THE CTLR CALLED ME BACK AND ADVISED ME TO CHK MY ALTIMETER SETTING; BECAUSE HE WAS GETTING A LOW ALT ALERT ON ME. I LOOKED AT MY ALTIMETER; AND SAW THAT I WAS AT 1000 FT AND LOOKING AT THE APCH PLATE; THE PROC MANDATES MAINTAINING 1700 FT UNTIL GS INTERCEPT. I BEGAN TO CLB BACK UP; AND RAPIDLY INTERCEPTED THE GS; AND BEGAN A DSCNT AGAIN. I THEN REALIZED THAT I HAD WANDERED OFF OF THE LOC AND REINTERCEPTED IT. AFTER A COUPLE OF DEVS FROM THE GS AND LOC; I BROKE OUT OF THE CLOUDS AT APPROX 500 FT AND LANDED ON RWY 24 WITHOUT ANY FURTHER OCCURRENCES. UPON TAXIING IN AND SHUTTING THE AIRPLANE DOWN; I CALLED APCH CTL ON THE TELEPHONE; AS INSTRUCTED. THE CTLR THEN ASKED ME WHAT HAPPENED; AND AFTER MY BRIEF DESCRIPTION OF THE EVENTS; ADVISED ME THAT I HAD COME WITHIN 400 FT OF ANOTHER ACFT. UPON FURTHER REVIEW OF THE EVENTS AS THEY OCCURRED; I REALIZE THAT THE SIT WOULD NOT HAVE BEEN AS SEVERE IF I HAD MAINTAINED A CONSTANT SCAN OF THE INST PANEL; AND TAKEN CTL OF THE ACFT FROM MY STUDENT SOONER. FURTHER DEVS FROM ATC INSTRUCTIONS COULD HAVE BEEN AVOIDED IF I MAINTAINED A BETTER SCAN; NOT FOCUSING SO MUCH ON THE FACT THAT THERE WAS A PROB WITH THE GYRO INSTS. ADDITIONALLY; THE AIR TFC CTLR'S ACTIONS OF GIVING ME A TELEPHONE NUMBER; AND INSTRUCTIONS TO CALL AS SOON AS I LANDED; DID NOT HELP THE SIT.