I was having this exact same issue with a similar system setup. I was about to give up, but I found a fix - run the game in Administrator mode.
The way I do it is navigate to the actual executable (the default location is C:\Program Files (x86)\Origin Games\Dragon Age\bin_ship). Right click on "daorigins.exe" and choose "Run as administrator". Since then, I haven't had a single crash, and I have all my video settings maxed now. You have to do this every time you run this (you might be able to make a shortcut that does this automatically, but I'd try it first to see if it fixes your problem).
Hope it works for you.