UNAUTHORIZED TKOF PERFORMED AFTER RWY INCURSION. UNAUTHORIZED RWY ENTRY OP.

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EDITORIAL TYPE PIC DECIDED TO GET CURRENT AFTER A LONG PERIOD (6 MONTHS PLUS) OF FLYING INACTIVITY. PREFLT WAS UNUSUALLY LENGTHY DUE TO AIRPLANE BEING IN SIMILAR SHAPE AS PIC; I.E.; ALL TIRES WERE HALF FLAT AFTER SEVERAL MONTHS OF SITTING ON THE LINE UNFLOWN. FUEL TRUCK HAD TO RETURN TO FBO FOR MORE AIR BEFORE TIRES COULD BE FILLED; AND FUELER DISCOVERED AN ENORMOUS BLACK WIDOW SPIDER IN TIRE WELL THAT HAD TO BE EXTRICATED BEFORE AIR COULD BE PUMPED. THEN; AFTER ENG START; PIC AND R SEAT PAX (A FLT INSTRUCTOR) SMELLED BURNING AND SHUT DOWN THE ENG TO CHK FOR BIRD NEST OR OTHER PROBLEM; BUT COULD DISCOVER NOTHING. WE MOVED THE FIRE EXTINGUISHER TO BACK SEAT SO THAT IT WOULD BE WITHIN EASY REACH. DURING RUNUP; 1 MAGNETO RAN ROUGH AND MIXTURE HAD TO BE LEANED TO CORRECT. BY THE TIME WE REACHED THE HOLD LINE AT RWY 29; I PIC WAS ANXIOUS TO GO. WE HAD AGREED THAT MY FRIEND THE FLT INSTRUCTOR WOULD HANDLE COM; BUT I CALLED TWR AND ASKED FOR TKOF CLRNC BEFORE HANDING OVER THE MIKE. THERE WAS NO ACTIVITY AT THIS POINT IN THE PATTERN FOR RWY 29; AND MY MINDSET INCLUDED 2 THOUGHTS: 1) THE TWR CTLR WOULD CLR US FOR TKOF; AND 2) MY FRIEND; BEING A FLT INSTRUCTOR; WOULD BACK ME UP ON COM. I NEVER DID 'HEAR' WHAT THE CTLR SAID. THE BOTTOM LINE IS THAT I TOOK OFF AND THEN HEARD FROM THE TWR AFTER TKOF THAT WE HAD NOT BEEN CLRED FOR DEP. OTHER RELEVANT FACTORS: MY FRIEND IS A LITTLE HARD OF HEARING AND MAY NOT HAVE COPIED THE CTLR'S INSTRUCTIONS. WE HAVE ALSO FLOWN TOGETHER SO MUCH THAT I EXPECT HER TO CATCH ALL MY MISTAKES AND; AT TIMES; AM NOT VIGILANT ENOUGH ON MY OWN BEHALF. IRONICALLY; THE LAST TIME I FLEW WITH HER WAS IN HER RETRACTABLE GEAR PLANE; WITH ME IN THE R SEAT SUPPOSED TO BE BACKING HER UP. ON 1 TOUCH-AND-GO WE ALMOST HAD A GEAR-UP BECAUSE SHE HAD FORGOTTEN TO PUT THE GEAR DOWN. IT WAS GREAT TO GET UP AGAIN; BUT MAYBE I'D BETTER FIND SOMEONE MEANER TO FLY WITH; AND VICE VERSA. P.S. I DID APOLOGIZE TO THE TWR LATER FOR NOT LISTENING WELL ENOUGH.