I'm somehow able to light an LED by touching it
This is probably AC leakage to ground trough your body.
You can measure this with an AC voltmeter, it often reads half the mains voltage.
This is not dangerous.  

It is caused by the Y-capacitor in switch-mode power supplies used to prevent emitting lots high frequency of noise.  

Example, CY1 2.2nF:


The solution to this is a grounded AC outlet. Secondary DC negative is then connected to ground, removing the weak AC component on the secondary.