What happens in subsequent openings if you click Window>Cascade, and then if it opens small click the top right corner for full screen?
The same thing happens.
It may be a preference corruption, then.
You may follow the instructions in Move the folder with Illy closed, and try to move the Workspaces file/folder only (I believe that is the name, I am still with 10), or the whole Adobe Illustrator XX Settings folder (XX being CS, CS2, CS3, or CS4, whatever you have).
Reinstalling does not replace the preferences, and I believe the Ctrl/Cmd+Alt/Option+Shift at startup does not change the Workspaces.
Ai use to open up a full screen when doing this...
Unlikely. This has been a known problem with Illustrator Win, and, to my knowledge, it has not been fixed... and here we are at version 14. I've railed about it for years, but now I've given up.
The last of those links contains a workaround I've been using, which entails starting AI via a batch file and changing the .ai file association to that batch procedure.
If you used to get a "full screen," you were just getting a "normal" (not maximized) window that was about the same size as your screen.
As with other discussions on this topic, we'll probably get contributors suggesting you set shortcut properties to start the app maximized, but you and I know that is not what we're talking about.