I've been watching this topic with great interest. I really must admire the patience and restraint shown by the other posters.
I really don't think our original poster is clear as to how 240 works, or on the difference between single phase and three phase. The starter he's using is massive - much larger than what he needs for the motor - so I think we're dealing with some salvaged equipment here.
With used equipment, all bets are off!
A 240v single phase circuit won't have a neutral with it. If the job was done in pipe, bringing in a neutral is no big deal. If Romex, MC, or some other cable was used, he's screwed .... time to re-wire.
Coil fried? This suggests some confusion as to how a starter is wired.
Another possible contribution to the problem might be the way the thing is switched. We can't assume a proper start / stop push button station is being used .... and the use of a cheap toggle switch just might be behind the coil burning up. Many toggles will let a minor amount of current through, even in the 'off' position
At some point, a man has to say "I'm lost," and call in a local pro to sort things out.