Whats this about RAM? You never mentioned any RAM issues. Please answer the following:
Have you tried each 970 by itself in each of the two slots you want to use?
Do they work one at a time in either slot?
What is the brand and model of your PSU?
Are you using the SLI connector between the two cards when trying both?
As I said, if each card works in either slot by itself but the two together cause the issue, then it sounds like the PSU can not handle the load.