Mini slayer exciter (tesla coil) not working
Polarity of secondary to primary matters.
D1 D2 need to conduct when secondary "fires".
Transistor base is driven negative when firing -
so BOTTOM of primary winding should go to transistor collector.
You have TOP going to collector. 

Swap connections to primary winding.
Stand clear.

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Added:

The 47K should go from base to V+ 

In your modified circuit you failed to keep the base to +ve resistor where it belongs. You now have it going from base to collector - as soon as the transistor starts to turn on it reduces base drive and the transistor enters a stable low current state.