U2415, Studio 14z (1440), DP/mDP no go

I'm having a similar issue with a Dell U2415 and a Dell Studio 14z (1440).  HDMI works fine to this display, but using the DisplayPort output with either the U2415's full-size or mini DisplayPort inputs fails.  I've tried multiple cables, and each time the display simply isn't detected in Windows, or it alternates every few seconds between being detected (although disabled) and disappearing, or it gets detected as a 640x480 display -- although even in that last case, no signal is ever displayed on the U2415 itself.

The issue is definitely compatibility between this particular system and this particular display, because I've successfully tested the following:

- Using the full-size DP and miniDP inputs on the U2415 with a Latitude E7440's miniDP out.

- Using the Studio 1440's DP output with a Dell U2410 display, using the same DP cable that did not work when the Studio 1440 was connected to the U2415.

So I've ruled out the Studio 1440's DP output port, the DP cable, and the U2415's DP inputs.  All of those work fine in other configurations.  As I said, using HDMI between the Studio 1440 and the U2415 works, but I want to use DP for a few different reasons.