Even though I guess I could get some downvotes for this answer, here we go :-)
function myParseDate(indate){ //indate in your format eg. '15-September-2011 13:37:00'
var datearraytmp1 = indate.split('-');
var datearraytmp2 = datearraytmp1[2].split(' ');
var datearraytmp3 = datearraytmp2[1].split(':');
var datearray = [datearraytmp1[0], datearraytmp1[1], datearraytmp2[0], datearraytmp3[0], datearraytmp3[1], datearraytmp3[2]];
var jsDate = new Date(datearray[2], monthStringToNumber(datearray[1]), datearray[0], datearray[3], datearray[4], datearray[5], 0);
}
var monthNames = {"January":0, "February":1, "March":2, "April":3, "May":4, "June":5, "July":6, "August":7, "September":8, "October":9, "November":10, "December":11};
function monthStringToNumber(monthname) {
return monthNames[monthname];
}
This will give you the jsDate as a JavaScript date object which you can use with fullCalendar without too much problem. N.B that monthNames need to be changed into your language.
It's an ugly but working solution.
Edit: A cleaner solution would be to use http://www.datejs.com/ which seems to parse your input just fine :P