@PraiseCats You don't need Origin in game to deal with this issue (many people actually find turning Origin in game off helps with some issues with DAI, especially if they're running the game on lower end systems), to make sure you're logged in in Origin, you want to alt + tab to the actual Origin application and make sure you're logged in. Or just make sure you're logged in/not in offline mode before launching Inquisition.
You also need to be logged in within the game itself. I don't actually remember where to do this (as mine just logs me in automatically and has done since I first installed it over a year ago), it may be in Options under the Account section. You must be using the same EA account to log in to Inquisition as you're using for Origin. You also need to use this same account for the DA Keep if you want to import world states.
If you're having issues connecting to the servers, make sure any anti virus/anti malware programs and your firewall are allowing both Origin and Inquisition to access the internet. Turning off any VPN or proxy you might be using could also help.
The only thing that stands out in your dxdiag is your CPU. It states that it's a dual core, minimum requirements call for a quad core. If the game works fine for you, though, then I guess it's not that big an issue. It shouldn't have any impact on your ability to contact the servers, as far as I'm aware.
Hopefully something in there helps. If not, feel free to come back and let us know. 🙂
