I am using a switching adapter input AC 100-240V, output DC 12V 2.0A to power my Arduino UNO.
I am measuring the voltage from my 5V pin and the GND pin next to it, and I am getting 8.6V, the 3.3V pin next to it is giving me 3.3V.
When I the USB to power it from my laptop, it works fine and I can get 3.3v from the 3.3v pin and 5v from the 5v pin, I am using a battery-powered multimeter to measure.
My guess would be that you have overloaded and damaged the Uno's on-board regulator by drawing too much current from the 5V pin when using the 12V PSU.
I am surprised the Uno is not completely dead, because the main chip cannot survive for long with 8.6V connected to it.
So like @LarryD said, where is this 12V being connected to your Arduino?
Is it the Vin pin?
Is it the power Jack?
Or in some other way?
Is the ground of this 12V being connected to the ground of the Arduino? It needs to be. If you are using the power jack this should happen automatically as the jack has two connections with the center pin being the positive.
Your photograph seems to show your board connected to the USB. I thought you said that works? So that is not really of interest to us. We need to see what it looks like when it doesn't work, so we can find out the mistake you made.
Don't actually turn the power on, just a look of the wiring will do.
Thanks for posting that, now we have a clear view of what is connected to what.
Tantalisingly out of shot is the power supply. The only thing I can think of that could be wrong is that this could have an AC output and not a DC one.
So I am forced to conclude that @PaulRB has it right in post #4 and your voltage regulator, or the capacitors around it has become faulty.
Or that your meter is set to read AC volts, which is unlikely because you measure the correct voltage when attached to the USB supply.