Hello Alison
The problem you have is the magnet on the push button corroded. It is the same problem I had with one of mine z240. (Sea attached picture of my push button magnet that has disappeared - it should be 2 to 3 mm out of the metal part.... As I saw on the button of my other strobe, but I have no picture...)
The push button, when pushed makes the strobe to ignor the pre-flash sent by the camera. As the magnet is corroded, the internal switch is not activated and the Inon strobe goes for a full flash when it gets the signal of the camera pre-flash, and when the camera flash signal is sent, the Inon strobe has not yet got the full charge and the inon strobe fires at a quite weak power.
The sensor of the camera is only active when the main flash fires, that's why it seams that the Inon strobe is not delivering the full power.
When you put the Inon strobe on STTL or STTl Low, the push button is ignored, that's why you can sea a full power flash.
Do not ask me why it got corroded. I do not know, although I think it might happened by the failure of a tiny o-ring on the button.
How to solve it... You can send the strobe to the Inon after sales service, or you can solve it by yourself, doing some DIY.
To be honest I am not happy with Inon service. I have sent the strobe to the dealer from whom I have bought a pair of Inons z240, the strobe has been sent to Japan (at least is what I have been told), I have payed 70€ and it came back the same, they said the strobe was ok.
I complained the the dealer and a magnet has been sent to me, so I would try to manage it by myself. I have not been able to take out the residual magnet on the button to put the new one.
So, I decided to figure out what is the screw dimension needed and looked for a screw. The measure needed is a M8x1.0x8
The magnet is a cylinder one with 4mm diameter, 7 mm long.
Be carefull to center properly the magnet on the screw, to grant that the screw can go all the way and the magnet gets inside a small depression the hole has in the middle.
I have bought the screw at eBay (http://www.ebay.co.uk/itm/160854075292?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1497.l2649)

Post script - I have bought other magnet and another screw, because I am thinking that it is a question of time that the other strobe I own gets the same problem....