WHEN A WITNESS ARRIVED AT THE ARPT, THE ACFT WAS AT THE FUEL PUMPS & THE PLT HAD THE PREHEATER ATTACHED. THE WITNESS RPRTD THERE WAS FROST ON THE ACFT & THE PLT BRUSHED THE LOOSE FROST OFF WITH HIS HANDS. THE PLT ASKED FOR A WINDOW SCRAPER, WHICH WAS PROVIDED, BUT THE WITNESS DID NOT KNOW WHAT HE DID WITH IT. AFT REFUELING, THE PLT STARTED THE ENG & REMAINED ON THE RAMP A SHORT TIME BFR TAXIING. A TKOF WAS INITIATED FROM THE 5300 FT RWY IN CALM WND CONDS. THE ELEV & TEMP WERE 9927 FT MSL & 2 DEG F. REPORTEDLY, THE ACFT ROLLED FOR MORE THAN 3/4 OF THE RWY LENGTH BEFORE BCMG AIRBORNE. THE WITNESS RPRTD THAT AFTER LIFT-OFF, THE ACFT DID NOT GAIN ALTITUDE, BUT REMAINED LOW, BGN A LFT TURN, THEN WENT DOWN.ANOTHER WITNESS OBSVD THE ACFT FALL FROM A LOW ALT & CRASH IN A LFT WING LOW ATTITUDE. A PAX RPRTD THE PLANE SEEMED TO SLOW DWN & LOSE ALT AFT TKOF, AS IF IT WAS TOO HVY. HOWEVER, DISREGARDING ANY FROST/ICE, THE ACFT WAS ESTIMATED 88 LBS BLO THE MAX WT LMT. NO PREIMPACT, MECHANICAL FAILURE WERE FOUND WITH THE AIRFRAME OR ENG.