I had something like this when i came to start my tt600 after a long time in storage.
In my case it was the starter relay/solonoid,which in your case should look like this :http://www.ebay.co.uk/itm/Starter-re...3a38a65&_uhb=1
I was able to take my tt600 relay apart,and just a clean up got it going.
To test yours, put a test light/multimeter between cable from relay to starter motor.When you press the start button it should light up/give a voltage reading.
If it does its the starter,if not then its the relay
The relay on my tt600 is just bellow the battery box area,follow the clicking noise !