A LR35 Captain reported that climbing to 10;000 FT the aircraft Compass froze and as the autopilot tried to follow an incorrect heading he became distracted and overshot his altitude.

Narrative

Departing and climbing to initial assigned altitude 4;000 MSL autopilot was engaged after 4;000 MSL and subsequent step climb to 10;000 MSL through various altitudes. At 9;000 MSL made a 1;000 FT to go call and noticed problems with HSI. The compass card not matching with the RMI; it froze at 180 degrees opposite to RMI and failed. No flags on the instrument observed. Autopilot started deviating to unknown heading. Autopilot in the heading mode was following the heading bug to a completely different heading. The altitude hold button was depressed at 10;000 MSL but the autopilot did not capture and altitude alert did not chime. At this point in time ATC alerted me to maintain 10;000 MSL. I noticed the aircraft was climbing through 10;000 MSL. Autopilot was disengaged and I took control of the aircraft to rapidly descend to 10;000 MSL. It took a few seconds to level off at 10;000 MSL. It was a series of failures in the equipment that compounded to the altitude infraction. Aircraft is going for maintenance today.