white vinegar? Havnt heard that one before. The white corrosion you are seeing is most likely leakage from alkaline batteries in which case killed the light. Another case may be a solder point broke at some point. I must have 8 or 9 mini Mag Pros and Pro Pluses. You should be able to unscrew the head off for a better look. Another possibility is a patina developed over the main contact points and is blocking current. Another suggestion is to buy a spray can of DeOxit Gold. A couple of spritzes with that stuff will clean any kind of patina/corrosion off of anything. If you are an owner of any kind of Mag be it mini or full on 4 D cell having a spray can of DeOxit gold is a must. For example corrosion can and will build up in the switches of my big D cell Mags blocking current flow or limiting it severely. I remove the rubber switch cover and do 3 short sprays down inside the center of the switch. The Corrosion dissolves instantly restoring full current.
So...screw off the head first and closely examine the LED and the wiring. Look closely for cracked or broken solder points. If it checks out okay clean ALL the contact points in the light DeOxit Gold would be the best choice to do it with but if you dont have access to it where you are take a bottle of rubbing alcohol and some Q-Tips, wet one end of a Q-Tip with the rubbing alcohol and wipe over all the contact points.
As for mini Mags they turn on when the threads inside the head make contact with the bare metal section below the threads on the tube. So...clean the threads in the head (the rubbing alcohol and Q-tip method should work fine) and make sure the bare metal section below the threads on the tube are clean. Remember to be looking for any sign of corrosion the whole time. Also unscrew the end cap and get a good look down at the head end of the tube where the batteries make contact with the bottom of driver. It most likely has corrosion on it.
Should you run into any corrosion DeOxit is really the only way to get rid of it I hope you have a store there that sells it.
Another tip-what keeps the LED and driver in place is a single O ring and the bottom of the reflector pressing down against it. Inspect the reflector. Unscrew the bezel and make sure the reflector hasnt somehow gone off angle. Also this all could be due to a loose bezel not holding the reflector down.
Once you have cleaned everything and made sure the reflector is in straight and that the bezel is tight and holding the reflector in place and down upon the driver buy a pair of Energizer Ultimate lithium AA's. Never use alkalines again. The Energizers crank max 1.5 volts per cell right up until they die and they dont leak. It sounds like at some point one of your alkaline batteries leaked and said leakage spread along the tube which is why you had the white corrosion on the bottom of the end cap. Chances are high that the leakage also made it to the contact point on the bottom of the driver.
Id say you have a 50/50 chance of saving the light. Most of the time raw alkaline leaked onto any point of the current path essentially destroys the circuit altogether as raw alkaline breaks down the metal of contact points. Even if you score some De Oxit Gold there is a good chance the alkaline has broken down any conducive metals to where they lose the ability to carry current.
Sucks for you man I know everything is expensive where you are. Here in Virginia I can go to Home Depot and get a new Pro Plus for 25 bucks. Every larger box and hardware store here carries some kind of Mag. Usually last gen D cell LEDs and even the old incandescent Mags. Does Home Depot or Lowes have stores in Australia? Here both HD and lowes also carry mini Mag upgrade parts from LED conversion upgrades to tail clicky switches so you dont have to turn the head to turn it on or off.
Just counted, I have 9 mini Mags all Pros and Pro pluses save for one old incandescent. Ive got lots of mini Mag parts etc. Hell if you cannot get yours to work Id be more than happy to give you one of mine I dont use them anymore anyways. They are all upgraded with glass lenses almost all of them have aftermarket tail clicky switches. Im much more into my 26 D cell Mags all modified of course. Ive got other small LED lights that took the place of my minis like the Fenix PD32 and the like.
and once again never use alkaline cells. Energizer Ultimate Lithium AA's give you more voltage, wont leak and they hold their charge for freaking ever.
Good luck