@pavlob69 Have you made sure you're not already logged in? Usually if you're not there will, I think, be a 'log in' button at the bottom of the main menu (has been... several years since I've had the game not logged in, so I may be wrong). It's possible it's just logged itself in. Is your DLC etc showing up in game? (Easiest to check is probably the Black Emporium, as I believe you can see that from Haven, and it's free).
No there is no ability to log on or off! I was well into a campaign and now it looks like I've lost it all as I was backing up to Origin cloud and can't get in to access it. Booh.
@pavlob69 So you're not logged in but there's no button/nag telling you to log in? That's weird 😛 Sure it used to nag me on the few occasions I got logged out due to internet going down or whatever. Pretty sure it was on the main menu. Has been a while, though, so I could be remembering wrong.
If your saves are still in the cloud, you will hopefully be able to get them back when you sort out your logging in issue (just be sure you don't tell it to use local saves when you start the game up, as it will overwrite whatever's in the cloud with whatever's in your save folder, which, it sounds like, is currently empty).
@pavlob69 Just started up the game (first time in a while) to see what it looks like when you're logged in. This is the front menu, logged in, on my game (after the 'connecting to servers' message when the game's loading):
There is no message asking you to log in or anything, due to the game being logged in, only a 'dragon age keep' button at the bottom in the lower left corner (and all it does is launch your browser and take you to the DA Keep site). Is this how yours looks? If you go to options > account, is the 'always log me in' box checked? If it is, perhaps try unchecking it, see if you are then prompted to log in the next time you start the game? I can't seem to find any option to log out, either, so I'm still thinking the game is automatically logging in to your account. Sorry if this is no help, just trying to figure out why you have no log in option unless you're already logged in. 😛
As for your saves, since you reinstalled everything and wiped them from your computer, you might want to check cloud saving is enabled for the game in Origin. Right click the game in your Origin library, go to 'Game Properties' then click on the cloud saves tab and check that the box to enable them is checked. Again, be careful not to overwrite your cloud saves with your local (empty) save data. Let us know how you go. 🙂