I am running 4x R9 290s and I had to upgrade from 4GB to 16GB to get it to run at all.
The thread concurrency for the 290s and 290x is usually over 30000 so you need a lot of RAM for the initial startup. Once it starts, RAM doesn't matter any more.
A way to test this is to set your thread concurrency really low to see if it starts properly. Maybe something around 8192 to start. If everything starts up that way but not when you set it to the default concurrency(30592 for mine), you need more RAM.
Thanks. I picked up 8GB over lunch and will add it this evening to see just how much I need. I'm hoping 8GB is enough, but will scale to 12 then 16 until I get it working. I heard somewhere that I cannot find now, 2GB/card usually works. Looks like I just have an evening full of playing with a rig ahead of me.