Good day,
The transformer is a bit low on voltage and current for a medium size coil (23ma @ 10kv) but will work however; the sparks may not be what you expect. A 30ma 15kv neon transformer @
http://cgi.ebay.com/Neon-Transformer-15000V-30mA-indoor-Tesla-Coil-/150598566984?pt=BI_Circuit_Breakers_Transformers&hash=item23105fc448 will give better results. It is hard to state what the issue with no sparks now due to limited information from this post; however, start with the transformer. Isolate the transformer from circuit and ensure it is unplugged from power supply and measure the secondary with an ohm meter. If the meter indicates an open circuit, the transformer maybe damaged. Did you have a Terry filter @
http://www.hvtesla.com/terry.html between the transformer and Tesla Coil, that is did you have a low pass filter and safety gap to ensure kick backs and RF did not get back into transformer? When the Tesla coil is out of tune, these kickbacks can be damaging indeed. The secondary wire of the transformer is very thin and can be damaged by these kickbacks if no protection. If the transformer measures a reading on the ohm meter, you can test the transformer output with few volts (AC) into the primary and measure the output. Since it is a 10kv transformer, just three volts on the primary, you should read 200 volts or so on the secondary of the transformer indicating the transformer is good. Ensure to use safety in measuring this voltage however, as high voltage can kill. If the transformer is still good, look at the spark gap to ensure gaps are not to far apart or carbon has built up on contacts increase resistance not allowing a spark across the gaps. Just work forward on each part of coil, first transformer, spark gap and then capacitors testing each part to ensure no opens of fried components.
Good luck,
Dr. Spark @
www.drsparksite.com