I downvoted the original comment because grammar pedantry adds nothing here. But if you're going to correct a pedant, you've got to be right. You're applying a test you don't understand and you messed it up.

"I" is the subject of the sentence, or the person who is doing the thing. "Me" is the object of the sentence, or the thing that is receiving the action. Since he and his friends are the ones who did the building, "I" is the correct pronoun.

Going back to the test you gave, the correct way to apply it is to replace entire the noun phrase with "I" or "me". The noun phrase here was "me and my friends together". "I built an 8 bit CPU" vs "Me built an 8 bit CPU". The former is the obviously correct one.