Similar problems. Bought an 05 TXT 300 fixer upper as the first step of my foray into trials.
Very hard to start - crash start only and overheating.
I replaced leaking head o-rings and leaking carb float and hoped all would be well.
No joy. Still difficult to start - crash starting in 6th only sure fire way. Still overheating.
Further investigation revealed that the fan was cutting out when engine RPMs were raised.
Checked that thermostat and fan were not faulty to rule them out.
Ducati regulator unit has two outputs - one for radiator fan and one for lights.
Noticed that green back of Ducati regulator was brown (looked to be caused by heat) in the area where the fan output originated.
Ran the fan off the lighting output and the fan would now stay on when engine RPMs were raised.
Overheating solved :-)
Obviously something wrong with regulator.
Still a nightmare to start though once started, it would happily idle and run OK.
Ordered replacement Ducati regulator from a supplier in Italy who did not mind posting downunder - not the easiest part to find.
Fitted new part.
Overheating cured AND starting with kick start :-)
Since then, still not the best starter and it was ruining my foray into trails. I took it to a wise mechanic who was good with trials bikes as I was running out of ideas.
He found worn jets and that the throttle slide had been modified. He attended to these and it starts much better now.
Bike is still not the greatest starter but I can start it and it doesn't ruin my day out like it used to. My friends can't start it so I get to show them up when I get it on 1st or 2nd kick. There is obviously a knack which I have largely acquired.
Lessons learned:
1. No substitute for methodically working through the ignition, compression, fuel triangle - there were faults in all these areas.
2. Per posts above, the Ducati regulated systems can have starting affected by a faulty regulator. Browning on the back is a good indicator of a fault.
3. Trials boots with an extra inner sole can take a lot of the starting pain away.