I think it sounds like the mic signal and headset ground lines are shorted together. The mic signal will be shorted to ground when both plugged into the same computer (i.e. shared ground)
When they don't share a ground, the problem goes away as the only common signal path is up to the short and should be of negligible resistance.
Testing with a multimeter would confirm this, just touch one probe to the tip of mic jack and other to headset sleeve (The other larger contact - I'm assuming mono TS Jacks, as opposed to TRS jacks)
Thanks to a certain theBear on IRC's freenode (#electronics), I learned that devices generally test for the presence of a microphone by checking the resistance across the bottom two pins.
There doesn't seem to be a consistent convention for pinout, but generally mic and ground occupy the two rings closest to the sleeve
so the device tends to check for the resistance between these bottom two rings to determine whether a microphone is present.
for a standard stereo plug (L+R+G), The resistance should be practically zero as there is just one single ring that will be connecting the G and M
so the host says ' if the resistance is < X, then we assume no microphone. '
clearly 100 ohm is too small a value for X
doubling up to 200 did the trick
I still didn't get it working on an android phone even trying 300. So I don't know what the deal there is.
in case anyone wishes to pursue this further, the advice I got was to try putting a potentiometer between the microphone and ground and turning it until the host registers that a microphone is connected
if you launch the sound recorder on your android device and sing while you are twiddling, at some point the spectrograph will just cut out -- this means that the device now believes a microphone is connected externally
the last suggestion was to string a capacitor in series with this small resistor. however I don't have any idea how to calculate what value to use
As a final note, the ratio of R1:R2 determines the ratio of V_in:V_out
Best Answer
The braid of the microphone cable may be disconnected at the plug.
The microphone cable braid, when properly grounded, shields the signal wires from electromagnetic interference/noise.
The ungrounded braid would itself pick up the interference/noise and couple it to the signal wires.
The cable connections are to be checked at both ends to confirm the cause.