I have a new computer and opened up a new gog account and also I have a new e-mail. How do I get my game from my old account to my new account. I cannot sign into my old account because I do not have the old e-mail account.

Looks like a difficult problem, not sure if there's a solution. But in any case, you need to contact support. Gog staff usually doesn't answer questions in this forum and other users can't help you with your problem.

If you can prove to them somehow your identity (some past proof of purchase etc.), they might be able to help you somehow.

Contact support here:
https://support.gog.com/hc/en-us/requests/new?form=account

Tell them that you dont have access to your old email address anymore.
Hopefully have same infos ready about your old account like when you created it...
how many games you had on it or a list of some games you definitely had on the account and ya even better as blotunga already said hopefully some proof of purchases (meaning credit card statement or paypal statements if you bought via them)