I've been working on getting an egpu working with my Dell e6440 for a couple months now. My e6440 has BIOS A.02 and is running Windows 10 x64 and has the dGPU. I have tried any combination of the three cards I have (gtx 570, gtx 560ti, and R9 270) with the two docks I have (GDC Beast V8.3 and a BPlus PE4C V3.0). With the exception of the R9 270, the eGPU is detected, the drivers are installed successfully, and no errors are reported in device manager (Haven't been able to successfully boot with the R9 270, but I strongly suspect it's an issue with the card as it gives me issues in a desktop environment). Even though everything checks out when I check in Windows, I can't get anything else to see or use it. Attached monitors don't work and no benchmark or system utilities see it. I have tried booting with it attached and trying to attach it after Windows boots, and both have the same result. I hope I'm not missing something completely silly here, as I see in the large post by Nando4 regarding the e6440 says, "A NVidia or AMD card is a straight plug-n-play implementation on a E6440."
I have already tried using both docks and both the gtx 570 and 560ti with a e6420 and both worked nearly effortlessly. I have also tried using a clean install of Windows on the e6440 with no effect.