They will generally want to see your DD214 to verify an honorable discharge. Since you have that, you are good to go. They will always want the DD214, even 50 years later. The law does not protect anyone with a less-than-honorable by making it "go away" after a few years. The effect of this is to protect those who have an honorable (a general discharge used to common for enlisted folks, and should not be held against you, especially if it was 15+ years ago).