I used to play DC Universe Online on my old computer outside of Steam. I am currently downloading DCUO through Steam and I was wondering how can I connect my old account with my Steam account?
There is no official way to tie in your DBG (Daybreak Games) account to Steam. The Steam ID does not work like it does with say WBID games (Batman: Arkham Origins, Batman: Arkham Knight, etc.) where it ties your Steam ID to your WB Games account. You will still have to log in with your Daybreak Games account (previously SOE) once you finished downloading the game to your Steam account.
By logging in through the Steam launcher, you will unlock the Steam Wallet payment option but that option only exists when you log in to your account with the Steam launcher. (ie: You cannot pay with your Steam Wallet if you do not launch the game via Steam.)