SABRELINER 80 FLC HAS HSI RMI FAILURE AND DEVIATES FROM ASSIGNED HDG DURING DEP.

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SABRELINER DEPARTED FROM SDL ON THE SDL 5 DEP FROM RWY 21. THE REQUIRED TURN TO 300 DEGS WAS MADE AFTER TKOF AND PHX DEP CTL WAS CONTACTED AS ASSIGNED BY SDL TWR. DEP CTL REQUIRED A L TURN TO 270 DEGS; SHORTLY FOLLOWED BY A FURTHER L TURN TO 250 DEGS; THEN 210 DEGS TO INTERCEPT THE 077 DEG RADIAL INBOUND TO BUCKEYE VOR. THE FLT DIRECTOR WAS IN USE AND THE HDG BUG POSITIONED TO 210 DEGS FOR THE REQUIRED INTERCEPT. THE PNF WAS IN THE PROCESS OF SELECTING THE REQUIRED FREQ FOR THE BUCKEYE VOR AND SETTING UP THE INBOUND COURSE OF 257 DEGS. IT WAS SOME TIME INTO THE TURN THAT IT WAS NOTICED THAT THE #1 COMPASS SYS DRIVING THE HSI HAD FROZEN AT THE 300 DEG INDICATION. BY THIS TIME THE ACFT HAD TURNED FURTHER TO THE SE THAN REQUIRED BY DEP CTL. WHILE SWITCHING TO THE #2 SYS; PHX DEP CTL ADVISED THAT WE HAD VIOLATED THEIR HDG REQUIREMENTS AND WE WERE GIVEN A PHONE NUMBER TO CONTACT THE SUPVR. WHEN WORKLOAD PERMITTED IT WAS FOUND THAT THE RMI CIRCUIT BREAKER WAS OUT. THIS WAS RESET AND ONCE AGAIN OVERLOADED AND DISCONNECTED AGAIN. THE FLT WAS TO HAVE TERMINATED IN SAN JOSE; CA. HOWEVER; DUE TO THE NAV PROBS; WE DIVERTED THE FLT TO LAS VEGAS FOR MAINT. AVIONICS PERSONNEL FOUND THAT THE PROB WAS IN THE HSI UNIT. WHAT FURTHER COMPLICATED MATTERS WAS THAT THE INOP FLAG FOR THE COMPASS SYS WAS NOT WORKING. THIS ACFT DOES NOT HAVE THE RMI REFED TO THE #2 C5 SYS; SO BOTH THE HSI AND RMI ON THE L-HAND SIDE WERE FROZEN AT THE 300 DEG POS. PHX CTL CTR WAS CONTACTED AND THE PROB EXPLAINED TO THEM. WE INQUIRED WHETHER THEY REQUIRED US TO FILE A RPT. THEY ADVISED THAT THE EXPLANATION WAS SUFFICIENT AND THE RPT WOULD NOT BE NECESSARY.