THE FLC OF AN LR35 LOST DIRECTIONAL CTL DURING TKOF WHEN THEY EXPERIENCED A BLOWN TIRE AT TKOF DECISION SPD. THE CAPT (PF) CITED DIM RWY LIGHTING AS A FACTOR IN THE RWY EXCURSION THAT FOLLOWED. TKOF ABORTED. ACFT DAMAGED.

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UPON ARRIVING AT THE RAMP FROM 'CREW QUARTERS;' THE CAPT COMPLETED THE PREFLT INSPECTION WHILE I POSITIONED MYSELF TO GET THE VFR CLRNC BACK TO JVY. AFTER RECEIVING THE CLRNC; WE WERE CLRED TO TAXI TO RWY 19. WITH MY PRIMARY ATTN DIRECTED TO COMPLETING THE 'BEFORE TKOF' CHKLIST AND AS THE ACFT WAS BEING POSITIONED ON THE RWY; I HEARD THE CAPT ANNOUNCE THE 'CTRLINE.' WITH THAT INFO; I QUICKLY GLANCED OUT OF THE COCKPIT TO SEE HOW EVERYTHING LOOKED. EVERYTHING LOOKED NORMAL SO WE BEGAN THE TKOF RUN. THE CAPT ANNOUNCED 'SET PWR;' SO NOW MY PRIMARY ATTN WAS DIRECTED TO SETTING THE CORRECT FAN SPD FOR THE GIVEN ATMOSPHERIC CONDITIONS. AS THE FAN SPD WAS SET; THE AIRSPD QUICKLY BECAME ALIVE; WHICH I ANNOUNCED. THE CAPT RELEASED THE NOSEWHEEL STEERING AND I VERIFIED THAT BY ANNOUNCING 'PANEL CLR.' THEN CAME THE 100 KT XCHK BTWN THE CAPT'S AIRSPD INDICATOR AND MY AIRSPD INDICATOR. WITH MY PRIMARY ATTN DIRECTED TO ENG OPERATING INDICATIONS AND THE FAST APCHING V1 AIRSPD; MYSELF AND THE CAPT HEARD A LOUD BANG. THE CAPT RESPONDED BY ASKING 'WHAT WAS THAT?' I QUICKLY RESPONDED BY SAYING 'I DON'T KNOW.' WITHOUT FEELING OR EXPERIENCING ANY DIRECTIONAL CTL PROBS; I ANNOUNCED 'V1.' NO SOONER THAN V1 WAS ANNOUNCED; THE CAPT ABORTED THE TKOF. WHEN THAT DECISION WAS MADE; I QUICKLY GLANCED AT THE ENG INSTS TO SEE IF A 'ROLLBACK' HAD OCCURRED; WHICH IT HAD NOT. WHEN PWR WAS DECREASED; THE NOSE APPEARED TO PITCH UP SLIGHTLY. MY FIRST VIEW INDICATED THAT THE ACFT WAS L OF THE RWY CTRLINE WITH THE CAPT CORRECTING TO THE R. ONCE THE AIRPLANE WAS DECELERATED ON RWY 19; WE TAXIED BACK INTO THE RAMP. OUR INITIAL ASSESSMENT OF THE EVENT WAS A CATASTROPHIC TIRE EXPLOSION BECAUSE AS WE TURNED INTO THE TXWY THE CAPT EXPERIENCED TURNING PROBS. WHAT I FOUND WAS THAT THE #4 TIRE WAS GONE. AFTER A CLOSER LOOK AT THAT ASSEMBLY; I NOTICED THAT PART OF THE HUB WAS MISSING; AS WAS THE LNDG LIGHT. THE STRUT ALSO APPEARED DAMAGED AS DID THE GEAR DOOR. MOVING BACK OVER THE L SIDE OF THE ACFT; I NOTICED A LARGE DENT IN THE LEADING EDGE OF THE WING ROOT; DAMAGE TO THE L MAIN LNDG GEAR; LNDG LIGHT MECHANISM; GEAR DOOR DAMAGE; AS WELL AS A 'GOUGE' ON THE L SIDE OF THE NOSE COMPARTMENT JUST FORWARD OF THE CAPT'S POS. AFTER ASSESSING THE DAMAGE; THE CAPT DECIDED TO REPOSITION THE ACFT TO ANOTHER RAMP. I QUESTIONED THE CAPT ABOUT THIS DECISION TO MOVE THE ACFT. THE CAPT'S DECISION WAS FIRM SO WE TAXIED. THE #3 TIRE EXPLODED PRIOR TO XING RWY 17. THE CAPT LIMPED THE ACFT ACROSS RWY 17; AND IT WAS THEN TOWED. SUPPLEMENTAL INFO FROM ACN 326457: CREW WAS TIRED AFTER 2 NIGHTS OF CARGO FLYING. RWY LIGHTING TOO DIM TO DEFINE RWY BOUNDARIES IN STRESSFUL; EMER SIT. ACFT'S LNDG LIGHTS NOT AS EFFECTIVE AS OTHER LEARS I'VE FLOWN.