"Downloadable Content is Missing"

@Kiro_Riley Are you playing while logged in to the DA servers in game (and also logged in to Origin on the same account)? The DLCs need to be authenticated online before they will be available in game, and saved games will not load if you don't have the necessary DLC available.

Whenever I try to log into the DA servers it says I have to be logged in on Origin first, which is stupid because obviously I have to be online in origin to be able to see the DA menu screen in the first place.

Weird thing though, I can log into the DA servers from DA:O just fine, but unfortunately it doesn't keep me online in the DA servers when I switch over to DA:I

Okay lets get part one taken care of first. Can you log in to the Origin application and be in ONLINE mode, and stay there until you choose to exit the app or go offline? If not, Origin seems to be having an issue for you. I would uninstall it and download a new copy from the "Download Origin" link at the top right of this page.

Uninstalling Origin will not affect you installed games, they will be visible in the new install of Origin when you log in.

I am absolutely able to go online in Origin, I can see the "Go offline" option and friends coming online and going offline

Okay, go to Application settings in Origin and make sure Origin in game is disabled for DAI. Then see if you can log in from the main menu of the game. If not you need to insure you are logging in to both with the same account. That can be found in game options.

I disabled Origin in game for DA but when I try to log into DA servers it still gives me the same message, "you must be logged in Origin to access online features," etc. 

And as for logging into both Origin and DA servers with the same account, in the DA:I menu when I click the log in button it doesn't even let me enter the login details, it just throws up the window telling me I need to be logged in to Origin immediately

@Kiro_Riley Do you have a firewall or anti malware program which could be preventing the game from accessing the internet? Do you use a VPN or proxy which could be getting in the way? 

Nope, neither

This sounds like a browser issue. Is Chrome or Edge by chance your default browser? If so change that to IE or Firefox, open origin and log in, then come here and sign in - sign out first if you normally stay logged in. Now see if you can log in in game.

My default browser was Chrome, so I changed it to IE, opened Origin.exe and logged in, signed into the Origin website through IE, opened DA:I and still the same message when I tried to log in to DA servers

I'm pretty sure that was the correct order so it probably isn't a browser problem