ENGINE WILL NOT TURN OVER, EVEN WITH A FULL BATTERY CHARGE AND JUMPER CABLES. THE STATER ENGAGES AND THE FLYWHELL TURNS ABOUT 1/4 REV. AND STOPS. IF I MANUALLY ROTATE THE ENGINE MORE THAN 1/4 TURN (PAST TOP DEAD CENTER?), IT WILL THEN TURN OVER AND START. IT WILL THEN START OK FOR THAT DAY OF MOWING BUT THE PROBLEM REOCCURS AFTER NOT USING IT FOR A FEW DAYS. WE HAVE CHECKED FOR BATTERY DRAW WITH THE IGNITON OFF AND HAVEN'T FOUND ANY.

Check the battery

Maybe problem with starter motor? It does two things, it kicks out the starter drive gear and spins. The flywheel usually has cover, remove the cover, try to see if starter drive gear engages the flywheel teeth, with key in the crank position.
Some of the national brand auto stores will test the starter for you. Sometimes, I take the starter off, lay it on the ground, hook up jumper cables properly from battery to starter motor. It should kick out the drive gear and spin, granted that is no load test. Intermittent issues can be a pain.
I just want to add, when working under a vehicle, safety is always your responsibility.

I just wanted to add, make sure battery has a full charge and battery connections all good.

Which is the problem, no fire, or no crank. No fire means to spark to engine, but engine turns over fine. No crank means engine won't turn over when key is turned. I'm assuming engine will not turn over. Three most common problems. 1. Weak battery (get tested at auto parts store). Will hold charge for short time once started, but loses it when sits overnight. 2. Bad starter. Possible but not likely, still not out of the question. 3. Bad battery cables. This is an easy test. Take a pair of jumper cables and bypass the battery cables by connecting black side of jumper cable to "-" of battery and block of engine, and red of jumper cables to "+" of battery and (tap) Battery terminal post on starter...engine should turn over. Ensure you take all safety precautions to prevent car from moving during this procedure. Best of luck resolving this problem.

Hi, just like to ask you to try something. Take out the spark plug or plugs and crank over the engine. This should not be a problem for the battery or starter. If this is ok and the motor turns over. Remove the starter motor and check the cog that engages with the engine flywhell to check it is in good condition. If it is damaged that may be the problem. If that is ok then just check that the battery is of the corect amperage ie the amp hours rating it might be that it is too small. Lastly if all those are ok then you might want to change the oil in the engine to one that is less viscous say 15 40. I personaly have had similar problems and tend to put the battery on charge say 1 hour before I want to use it as I sometimes take it to a friends to do their grass. Very last I put the accelerator at half way turn the engine over and pull out the choke as the motor starts to turn. Hopefully these tips will give you a result.
Steve

you mean it wont crank, it must crank to start.
1: bad starter system
2: weak battery even a new battery can be weak.
if you dont charge it first.
or if it starts ok then wont later, that means cars charge system failure.

can you jump start engine? with jumper cables.
that be a big clue there, proving starter works but battery was weak.
if the battery is fully charged.
you can hot wire the starter solenoid, (tiny terminal)
if car cranks now, the key start wire is failing.
A/T or M/T tranny? both use different path here....??????

if you cant hot wire it, then that means the stater is bad
the cables bad or the battery is not really connected.
or possible the engine is seized, can you hand turn over the engine at the front crank bolt (CW , facing rear, in neutral)
if not motor is seized.
some times even the starter and rig gear can be seized.
the starter can be bench tested. too.
http://www.fixkick.com/nocrank.html

NICE TOUCH WITH THE CABLES BUT ALWAYS USE A METER FOR A COOL TWENTY BUCKS AT THE PARTS STORE TO SEETHE LEVEL OF THE BATTERY ABOVE AND BEYOND 12.90 VOLTS IS USUALLY REQUIRED BUT FULL CHARGE IS WHAT YOU NEED ALWAYS. IF THE CHARGE WONT HOLD ON A ACTUAL "BATTERYLOAD TEST" BITE THE BULLET AND GET A BETTER BATTERY

Instructions

1. • 1 Remove the seats from both motorcycles to access the battery. Use an Allen wrench to remove the bolts from beneath the rear of the seats' padding. Use the ignition key to release the seat lock found on an earlier GSX-R600 model.
     
   • 2 Start the working motorcycle and clip the red (positive) jumper cable to its positive battery terminal. Clip the opposite end of the red jumper cable onto the GSX-R600's positive battery terminal.
     
   • 3 Clip the black (negative) jumper cable to the working motorcycle's negative battery terminal. Clip the opposite end of the red jumper cable onto the GSX-R600's negative battery terminal.
     
   • 4 Rev the working motorcycle's motor to 3,000 to 4,000 RPM, while in neutral, to produce enough power to maintain an electrical charge. Maintain this engine speed for the remainder of the procedure.
     
   • 5 Press the starter button on the right handlebar to start the GSX-R600's motor. Release the button immediately if the motorcycle does not start within five seconds then try again.
     
   • 6 Rev the GSX-R600's motor to 3,000 to 4,000 RPM and maintain this engine speed for at least three minutes.
     
   • 7 Disconnect the black jumper cables from both motorcycles, followed by the positive jumper cables. Reinstall the seats on both motorcycles, using the reverse method of removal.
     

Instructions

1. • 1 Remove the seats from both motorcycles to access the battery. Use an Allen wrench to remove the bolts from beneath the rear of the seats' padding. Use the ignition key to release the seat lock found on an earlier GSX-R600 model.
     
   • 2 Start the working motorcycle and clip the red (positive) jumper cable to its positive battery terminal. Clip the opposite end of the red jumper cable onto the GSX-R600's positive battery terminal.
     
   • 
     
   • 3 Clip the black (negative) jumper cable to the working motorcycle's negative battery terminal. Clip the opposite end of the red jumper cable onto the GSX-R600's negative battery terminal.
     
   • 4 Rev the working motorcycle's motor to 3,000 to 4,000 RPM, while in neutral, to produce enough power to maintain an electrical charge. Maintain this engine speed for the remainder of the procedure.
     
   • 5 Press the starter button on the right handlebar to start the GSX-R600's motor. Release the button immediately if the motorcycle does not start within five seconds then try again.
     
   • 6 Rev the GSX-R600's motor to 3,000 to 4,000 RPM and maintain this engine speed for at least three minutes.
     
   • 7 Disconnect the black jumper cables from both motorcycles, followed by the positive jumper cables. Reinstall the seats on both motorcycles, using the reverse method of removal.
     

Disconnect and clean the battery termials and cables then reconnect the cables. Connection could be dirty. If that doesn't work make sure the battery has a full charge over 12v with a volt meter. If you have some jumper cables jump it from another battery.

Is the oil sump full? Has it been run with out oil? You can do an amp draw test on the starter. Should be 60 amps or so. Can you roll the engine by hand? If engine turns free pull the starter out and bench test it with jumper cables. Positive cable to cable lug and negative cable on the starter case. Hang on to it, lots of torque. If the stater turns slow or gets hot it is probably bad.