B737 FLC REJECT TKOF SRQ RWY 22 WHEN OBSERVING A PA28 LAND OVER IN FRONT ON SAME RWY.

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RWY 22 AND RWY 14 BOTH IN USE. PREDOMINANTLY LIGHT SINGLE ENG ACFT; HOWEVER SEVERAL CPR JETS ALSO USING RWY 22. OUR OPS REQUIRE RWY 14; WE WAITED SEVERAL MINS TO BE CLRED INTO POS AND HOLD ON RWY 14. FINAL APCH WAS CLR WHEN WE TAXIED ONTO RWY. WE HELD IN POS FOR SEVERAL MINS WHILE OTHER ACFT LANDED RWY 22. WHEN CLRED FOR TKOF; PWR WAS ADVANCED JUST AS WE STARTED TO ROLL ON TKOF; A SINGLE ENG PIPER PA28 FLEW OVER OUR ACFT AND LANDED ON RWY IN FRONT OF US. APPARENTLY THIS ACFT WAS NEVER IN CONTACT WITH SRQ CTL TWR. TKOF WAS DISCONTINUED TO PREVENT A COLLISION WITH OTHER ACFT ON RWY. I WILL BE VERY RELUCTANT TO ACCEPT A TAXI INTO POS AND HOLD CLRNC IN THE FUTURE DUE TO BEING UNABLE TO VISUALLY CLR FINAL APCH PATH PRIOR TO COMMENCING TKOF ROLL. NONE OF OTHER ACFT WAITING TO DEPART RWY 14 BEHIND US WERE AWARE OF THIS ACFT ON FINAL AND TWR CTLR STATED HE SAW THAT FINAL WAS CLR PRIOR TO ISSUING TKOF CLRNC. SUPPLEMENTAL INFO FROM ACN 534150: TWR FOUND OUT THAT SUBJECT ACFT SAID HE'D LOST ELECTRICAL PWR; RADIOS; AND DIDN'T KNOW HOW MUCH FUEL HE HAD REMAINING. WAS A STUDENT; WHO'D LOST HIS SITUATIONAL AWARENESS.