I recently purchased an AMD R9 290 and like many people I suffered the black screens and BSOD's after install.
After much digging and reading the tons of other people that experienced the same issue, I then completely removed the driver with the Guru3D Display Driver Uninstaller. I allowed it to restart my PC, I was then presented with a Windows logon screen, already further than various attempts before.
The next step was installing the latest Beta driver from AMD http://support.amd.com/en-us/download.
The important part of installing this was to Only install the driver. Nothing else, no AMD video, not HDMI (because I use DVI, I guess it would be okay if you're using HDMI), and especially not installing Catalyst Control Center (CCC). Various installs of this on fresh copy of windows regularly seemed to result in CCC crashing when installing first time.
With the driver installed, and hopefully not a black screen, restart Windows. At this point it should be okay to re-run the installer with CCC enabled.
One of the other things that may be relevant to the BSOD issue is the layout of power pins.
There's an 8 pin connector on an R9 290 and a 6 Pin. I simply used a 6 and a 6+2 pin connector from my PSU and assumed all would be fine, but apparently not. The adapter cable supplied with my card was not a 6 to 8, but a 6 to 7 pin adapter. See below image:
This seemed to solve the BSOD and the buggy BIOS I was getting on POST. By buggy BIOS, I mean tearing, slight unresponsiveness, and an overall generally slow POST.
Hopefully this can help someone else out there get thier card working without an RMA.