The proper way is to take plastic cowl off unplug (white plug with black jack plug) it and check for the continuity of each turn, plus check your dash lights to see if they all disapear after turning the engine on.
Hard to say mate..... but from what I know there is a constant 12V to the starter, but its switch from the spade is what starts it and cuts it out after a few seconds?
Usually if the ignition switch is broken there is no voltage on the spade to open the contacts to allow the solenoid to be powered up. What I'm thinking is your solenoid is sticking open and its got constant 12V to the spade and turning the starter on all the time?
Hence send it back whom ever you bought it from?
If you have a voltmeter you could check if all contacts on the starter has continuty on all the contacts becuase that spade should be switchable only from ignition. If all contacts beep then something is stuck and you have constant open circuit!