The setup you have described should be supported.
Is the DP-DVI adapter working when it is in the only display connected? If so, it could be that when having three displays connected it is not working as an active.
The R7 370 supports a maximum of two passive display connections, HDMI/DVI. The third display must use a native DP-DP connection, or a DP-DVI active adapter. Perhaps the adapter you picked is incompatible. We have tested and supported adapters available here > AMD Eyefinity Technology - Recommended Adapters
Thanks for the advice.
The adaptor did work when its was the only display so it makes no sense to me.
Anyway bit the bullet and went a brought a new monitor with display port and now it works a treat.
Glad to hear it.