I lost my old Steam account, and all the games on that account. Can I link Steam up with those old games for my new account or do I have to buy them all again? If there is a way to re-sync my games, how do I do it?
When buying a game on Steam, you are buying a license for that game for that specific account. You cannot "sync" the games you still have on your computer, because you do not own a license for it.
If you simply have trouble logging into your account, consult this page of the steam support website. It contains options to recover lost passwords, lost account name, hijacked accounts and even lost mobile authenticators.
If you lost your account due to a ban, breach of terms of service or do not have access to anything associated with your account anymore (including email), then you are out of luck. Take better care of your account next time, especially if it contains anything of value.
Delete the new empty junk account you created. it will just mess things up for.
and follow the instruction on recovering your old account.