With Apple now changing their "Build Number" with every tiny little update we have had problems with the unsupported cards that require the Nvidia Web Driver. The root cause of this issue is the fact that Apple has stubbornly refused to add any additional cards into the OS X default drivers. The last OS that got new Nvidia cards was 10.8.5, believe it or not.
So, for all of 10.9 and now all of 10.10 any Nvidia card introduced after the GTX780 and GTX Titan has to have the Nvidia Web Drivers installed to run. Specifically:
GTX Titan Black
GTX960/970/980 (Requires 10.10 or later and Web Driver)
GTX Titan-X (Requires 10.10 or later and Web Driver)
If these cards have no EFI, you will never see anything without the Web Driver. If you have EFI, you will see the initial boot screen and progress bar but the machine will crash before reaching the desktop.
The Nvidia Web Drivers are matched to a specific "Build" of OS X. As a "for instance", when 10.10.3 was released it was Build 14D131, a day or two later when it required a "Supplemental Update" this changed the Build Number to 14D136. The new Build Number requires a new Web Driver.
You can find your "Build Number" by going into "About This Mac", then "System Report". Next, click on the "Software" tab and you will see the image with this post. The top line has the information that you need. System Version: OS X 10.10.3 (14D131)
So if I was looking for the right Web Driver for the machine in the image I would look for the one for 14D136.