Measuring electric current in shield
Okay, let's think of the simple circuit: Your computer's chassis is the voltage source, you are the resistor, with your feet connected to the ground. To find the current, you'd normally measure the resistance &amp; voltage between your finger and feet, and divide them to find the current, right?
However, this is not the case for human body. Human body has a non-linear resistive characteristic. What does it mean?

Your multimeter finds the resistance between the probes by using a battery, a DC voltage source. The low DC current is likely to pass through the outer layers of your skin, which has higher resistance.

However, for higher voltages, your resistance is not the same. As voltage increases, the current will flow deeper inside your skin, and if it reaches your blood vessels, your resistance suddenly plummets. That's why your multimeter will show your resistance as megaohms, but you die when you grab 220 V grid...

So, your current measurements will most likely fail. You can measure the DC voltage, relative to your ground pin in your power outlet, but I think your house or power outlet has a problematic grounding, so this may not yield a good result.  Simply, in my opinion, you cannot have a reliable result by any means.