You might like to check out a similar problem is a Husky & Dixon forum
http://www.lawnmowerforum.com/showthread.php/47586-Yahoo-Kees-48-in-model-48172
To be of any help we will also need a copy of the wiring diagram that you are using so please post it.
If it is a pdf use the attachment button , if it is a photo/image then use the picture button.
If you have a 3 pole solenoid ( two big bolt on & one small usually spade ) then the solenoid makes the ground contact via the body of the solenoid.
Run a jumper from the battery - to the solenoid body when it is getting 12 V on the trigger wire.
IF it energises and energises the starter motor you have a bad ground, either on the mower itself or on the solenoid.
The other wires on those switches , the black , or brown ones are kill wires that ground the magneto.
If you have accidentially sent 12 V down them then the control chip in the magneto will be fried.
When jumping switches it is very important to remove the kill wires from the coils to prevent this happening.
Even the signal from some cheap ohm meters can fry the chip.
So do not be surprised if you no longer have a spark.
Also take note without the kill wires connected you are relying on the fuel shut off solenoid to turn the engine off.