earphones wiring button
This is just a guess.  As always without the proper "tools" there is the possibility of causing permanent damage.  I would avoid pushing any in-line buttons during this test. I might try connecting only the red/green pair from the jack to the red/copper pair from the phones.  If this produces sound in one ear phone leave the connection alone (point A).  If it does not, I would then connect the red/green pair from the jack to the blue/copper pair from the phones (that would be the same copper phone wire).  If this produces the expected sound leave it alone (point B).  If it doesn't then I'm stumped (stop).

If there is sound coming out of 1 ear phone after getting to "point A", I may next try connecting the copper/green pair from the jack to the copper/blue pair from the phones (that would be the same copper phone wire).  If there is the expected sound from both ear phones, I think we are done.  If not, keep going.

If there is sound coming out of 1 ear phone after getting to "point B" or if continuing from above, I may next try connecting the copper/green pair from the jack to the copper/green pair from the phones.  If there is the expected sound from both ear phones, I think we are done.  If not then I'm stumped (stop).

If successful, you may want to consider connecting any shielding wire.  Shielding is not necessarily needed for the phones to function unless it is used as a ground reference.  And is usually not critical as its primary purpose is to mitigate noise problems.

Last note, the above description is very specific with respect to the wire colors and your good description of how they appear in the cables.  So even if this does work, it may not work in general (for everyone).  But the procedure of trying 1 thing at a time is an important component of almost every problem solving procedure.