I just signed up as a new user using my current e-mail address. As I played around, out of the depths of my memory I recalled my old account information from when I originally signed up in 2000. I have logged into my old account but can't change the e-mail address to my current one because I created the new account using it.

Is there a way to delete my new account so I can update my old?

No, you cannot delete your account.
You can however fill in a garbage email address in the other account's email. Email addresses aren't validated (as of yet at the time of writing).

Thing to remember: the email address is the single unique identifier. The account name can be anything, we can all be called Jan on here and no one would know who's who.
So what you could do is:

1. Change the email address on your other account to garbage, even a@a.co will work.
2. Remove the computer from BOINC.
3. Change the email address on this account to the one you previously used on the TIOT account.
4. Add your computer to BOINC, using "Yes, 'existing user" and the email address and password you set for this account.
5. If needed, you can now change the name of this account to TIOT as well.

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Tengo un problema muy similar, ¿entendí correctamente la respuesta?:

En pocas palabras, la cuenta vieja la puedo utilizar para entrar a SETI y la cuenta nueva puede estar registrada pero no sirve de nada si no la vinculo a mi PC?