PLT OF A PIPER PA23-250 OVERSHOT CLB ALT ON DEP DUE TO DISTR FROM AN AVIONICS PROB AND MISUNDERSTANDING OF CLRNC ALT. ATC NOTED ERROR UPON RPTR'S REQUEST FOR A HIGHER ALT.

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WE DEPARTED MKC ENRTE TO MO49. OUR IFR CLRNC WAS 'AS FILED MAINTAIN 3000 FT EXPECT 5000 FT WITHIN 10 MINS.' OUR TKOF; CLB AND VECTOR ON COURSE WERE NORMAL. SOMETIME AFTER OUR CHANGE TO DEP CTL; WE WERE CLRED TO CLB TO 5000 FT. AS WE APCHED 5000 FT I ASKED THE PNF TO REQUEST 7000 FT. AT THAT POINT; ATC SAID HE HAD CLRED US TO 4000 FT -- NOT 5000 FT. I HAD UNDERSTOOD 5000 FT; HAD WRITTEN IT DOWN AND SET THE ALT ALERTER TO 5000 FT. WE TOLD ATC WE HAD UNDERSTOOD THE CLRNC TO BE 5000 FT -- NOT 4000 FT. THE CTLR THEN TOLD US TO 'JUST STAY AT 5000 FT AND I'LL WORK ON HIGHER.' END OF INCIDENT. I WAS DISTRACTED DURING EARLY CLB BY AN AVIONICS PROB AND HAD ASKED PNF TO HANDLE ATC COMS. IT IS POSSIBLE THAT I MISUNDERSTOOD; SET THE ALT ALERT AND CLBED TO 5000 FT WHEN IN FACT I HAD BEEN CLRED TO 4000 FT. PERHAPS THE FACT THAT I HAD BEEN EXPECTING 5000 FT WITHIN 10 MINS; PER THE ATC CLRNC RECEIVED PRIOR TO TKOF; LURED ME INTO THE ERROR. THE PNF AND THE ATC CTLR WERE APPARENTLY NOT AWARE OF THE PROB UNTIL I REQUESTED THE CLB TO 7000 FT. LOOKS LIKE TRIPLE HUMAN FAILURE INDUCED IN THE COCKPIT BY OUR AVIONICS DIFFICULTY AND FOR UNKNOWN REASONS IN THE ATC FACILITY.