There's a pretty severe delay with forum emails currently (being worked on), which might be the cause of it. You should still be able to post and browse the forums without having gotten the confirmation email. Check back on it in a few hours or tomorrow and you may find it. Also be sure to check your "Promotions" and "Social" tabs if you have them (if using Gmail).
As an aside, email addresses are pretty easy to get and cost you nothing. If you really can't get the confirmation email to your current email address, I'd suggest getting a Gmail or Yahoo account. Heck, go old-school and get a hotmail address. The signup process should take you all of 5 minutes.