Replacing old 4-way switch
&quot;all 4 wires are yellow&quot; -&gt; an electrician after my own heart!  Those are my preferred colors.
Here is how 4-ways are wired.

As you see, the yellow wires (yours actually are that color) come from 2 different places. A pair of yellows comes from one place, and a pair of yellows comes from another place.
Your setup will be in conduit, since nobody makes yellow-yellow-red cables... and much of Chicagoland requires metal conduit.  (that's why there are no ground WIRES; the metal conduit is a superb ground).
So it's as simple as identifying the two pairs.  That's easy because each pair will be in a different pipe.  Hook up the 2 black screws to one pair.  It's downhill from there.

If they're all in one pipe, then yikes. The installer should have done something to mark them as pairs.  Look for black and brass screws on the old switch.
Worse comes to worst, if you have to decrypt this, make a test apparatus. Lop the plug end off a $2 extension cord, and plug a night light into it. Simple night light, not a smart light-sensor job.  Split the wires for about 8&quot; and strip the ends. Mark the ribbed wire white and the non-ribbed wire black.
Illegally attach the white wire to the metal of the junction box, i.e. by abusing a mounting screw.  Connect the black to one of the yellows.  (all with the power off, of course).
Turn the power on, and see if the light lights.  Then run around and flip 1 switch at a time, checking in between every switch throw.  If that light comes on in certain switch positions, you have identified a supply-side yellow.  Turn off power and do it all again with the other 3 yellows to identify the other supply-side yellow.  Now, mark those two with black electrical tape for next time!