BE9L PLT ENTERED RESTR TFR AIRSPACE WHILE FOLLOWING ATC VECTORS WHILE ON AN IFR FLT PLAN. THE ACFT SLAVED COMPASS SYS WAS MALFUNCTIONING; PRODUCING INCORRECT HDGS.

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ON MAY/WED/03; UNDER MY CALL SIGN XYZ; I DEPARTED HRI VFR UNDER VMC CONDITIONS ON A PART 91 FLT TO RDM. AFTER FINISHING WITH MY BEFORE TKOF FLOWS AND CHKLIST (WHICH INCLUDED CHKING MY HSI AGAINST THE RWY HDG); I DEPARTED RWY 22. AWARE OF THE RESTR AREA W OF THE ARPT; UPON REACHING 400 FT AGL; I TURNED TO A L CLBING TURN WHILE COMMUNICATING WITH CHINOOK DEP ON FREQ 133.15. AS I CONTINUED MY CLBING TURN TO THE SE; THE CTLR ASKED ME IF I WAS AWARE OF THE EXISTING TFR. MY REPLY WAS 'AFFIRMATIVE;' AND A XPONDER CODE WAS ASSIGNED TO MY ACFT. AFTER PROPER INDENT BY CHINOOK DEP; I WAS GIVEN A HDG AND AN ALT TO CLB TO. AFTER RADAR CONTACT WITH CHINOOK; I FOLLOWED THEIR COMMANDS; WHICH CONSISTED OF SEVERAL HDG CHANGES. AFTER A FEW MINS; IT BECAME APPARENT TO THE CTLR THAT SOMETHING WAS NOT QUITE RIGHT; AS I WAS GETTING VERY CLOSE TO THE RESTR AREA EVEN THOUGH HE WAS TRYING TO KEEP ME AWAY FROM IT. AT THIS POINT; I WAS STILL VMC; FLYING OVER A BROKEN LAYER WITH AN IFR CLRNC TO RDM. AT ONE POINT; I WAS ABLE TO SEE THE MIL RESTR AREA THROUGH THE CLOUDS RIGHT UNDER ME. IT WAS THEN THAT I TOLD THE CTLR I THOUGHT I WAS EXTREMELY CLOSE TO THE TFR; AND ASKED HIM FOR ANOTHER HDG TO KEEP ME CLR OF IT. IT WAS AT THAT POINT THAT BOTH; THE CTLR AND MYSELF; BECAME AWARE THAT MY HSI WASN'T WORKING PROPERLY AND THAT EVEN THOUGH I WAS COMPLYING WITH HIS COMMANDS; MY BROKEN EQUIP WAS HEADING ME INTO THE RESTR AIRSPACE. I NEVER GOT ANY RED FLAGS INDICATING THAT MY HSI WAS NOT WORKING; AND THE BROKEN LAYERS OF CLOUDS UNDER ME RESTR MY ABILITY TO RECOGNIZE ANY LANDMARKS TO ASSIST ME IN IDENTING THE TFR. UPON LNDG IN RDM; I CALLED MY MAINT DIRECTOR TO INFORM HIM ABOUT THE MALFUNCTIONING EQUIP. DURING MY LAST LEG OF THE DAY; GOING FROM RDM TO PDX; I DID NOT EXPERIENCE ANY PROBS WITH MY HSI. I THEN CALLED MY MAINT DIRECTOR AGAIN UPON LNDG AT PDX TO INFORM HIM THAT DURING THAT LEG THE HSI WORKED FINE. HE INFORMED ME THAT THIS IS TYPICAL OF A GYRO EXPERIENCING DETERIORATION AND THAT HE WOULD KEEP AN EYE ON IT.