A PA60 PILOT WAS DISTRACTED BECAUSE THE GEAR UP LIGHT DID NOT ILLUMINATE AFTER TAKEOFF. WHILE TROUBLE SHOOTING THE PROBLEM IN WEATHER AND TURBULENCE AN ALT DEVIATION OCCURRED.

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I TOOK OFF AND CLBED TO 1500-2000 FT AND CONTACTED APCH FOR MY CLRNC. THE CTLR CLRED ME TO ZZZ VIA VECTORS. CLB MAINTAIN 3000 FT; EXPECT 9000 FT IN 10 MINS. SHE GAVE ME A HDG; I BELIEVE IT WAS 030 DEGS. I THEN NOTICED THE GEAR-UP LIGHT WAS NOT LIT. I BEGAN CHKING THE HYD PRESSURE; IT WAS VARYING MORE THAN NORMAL. I WAS TRYING TO SEE THE REFLECTION OF THE NOSE GEAR ON THE SPINNERS; BUT I COULD NOT SEE VERY CLRLY BECAUSE THE SPINNERS WERE A LITTLE DIRTY. I WAS TRYING TO DETERMINE IF I NEEDED TO CYCLE THE GEAR. THE CTLR HANDED ME OFF AND I WAS GIVEN ANOTHER HDG AND CLRED TO ZZZ VOR. I BEGAN TRYING TO INPUT ZZZ VOR ON THE GPS. THERE WAS MODERATE TO SEVERE TURB SO I WAS HAVING DIFFICULTY DIALING IN THE INTXN AND I ASKED FOR A VECTOR TO THE INTXN. I WAS GIVEN A HDG; 340 DEGS I THINK. I WAS STILL WATCHING THE HYD PRESSURE AND TRYING TO TROUBLESHOOT WHY THE GEAR UP LIGHT WAS NOT ON. I WAS GIVEN A NEW ALT; 5000 FT AND NEW HDG. I WAS USING THE AUTOPLT. WE DO NOT HAVE ALT SELECT SO I WAS USING ATTITUDE UP ON THE AUTOPLT FOR THE CLB TO 5000 FT AND RETURNED MY ATTN TO THE GEAR UP LIGHT; ROTATING THE KNOB AND PRESSING TO TEST THE BULB. IT WAS OK. I WAS CHKING THE SPINNERS FOR THE REFLECTION OF THE GEAR DOORS TO SEE IF I COULD TELL IF THEY WERE CLOSED. THE CTLR CALLED AND SAID THAT MY ALT WAS SUPPOSED TO BE 5000 FT AND HE GAVE ME ANOTHER HDG AND HANDED ME OFF. I CHKED MY CLB; I WAS AT 5400 FT. I CORRECTED ALT; TURNING OFF AUTOPLT. I CHANGED FREQ; CTLR ASKED DEST; I REPLIED ON ASSIGNED HDG. HE CLRED ME TO AN INTXN; I ASKED FOR A VECTOR. HE CHANGED MY FREQ AND SAID I WOULD GET A VECTOR FROM THE NEXT CTLR AND CHANGED FREQ; GOT A HDG. THIS WHOLE TIME I WAS ALSO CONCERNED ABOUT THE POSSIBILITY THAT THE BRAKES MAY HAVE BEEN PARTIALLY CONTACTING THE ROTORS ON TKOF AND COULD HAVE OVERHEATED; MAYBE EVEN BE ON FIRE INSIDE THE WHEEL COMPARTMENTS; SO I HAD A LOT OF DISTRS GOING ON. I NEVER DECLARED AN EMER OR SYS MALFUNCTION. THE GEAR UP LIGHT NEVER CAME ON. I EVENTUALLY GOT FAR ENOUGH THAT I WAS ALLOWED TO GET ON COURSE AND CLB TO 9000 FT. THERE WAS MODERATE TURB THE ENTIRE RTE. WHEN I LANDED AT ZZZ; I DISCOVERED THAT THE NOSEWHEEL STEERING LINKAGE BOLT HAD SHEARED OFF AND THE NOSEWHEEL WAS A LITTLE OFF CTR AS IT RETRACTED. THE GEAR DOOR DID NOT CLOSE ALL THE WAY; SO THE GEAR UP LIGHT DID NOT COME ON. IF I HAD TO DO THIS OVER AGAIN; I WOULD HAVE ADVISED ATC THAT I HAD A SYS MALFUNCTION AND THAT I WAS WORKING ON THE PROB.