FINALIZE Migration of WordPress site (within GoDaddy account)

Hey, I'm migrating a site from one GoDaddy server to another (same account/user). All the files and DB are on the new server already, and displaying correctly, but when I go to redirect the DNS records and have them point to the new IP, both sites go down (and stay down). I don't know TOO MUCH about DNS changes, and I don't have the time now to resolve this. I would PREFER for whomever takes this "gig" to EXPLAIN TO ME how to go about resolving it all. If that's really not possible, I can create and distribute the necessary credentials, I just REALLY want to avoid unnecessary down-time from people re-trying what I've already done. Ultimately, I'm not 100% sure on DNS work, and I HATE working with GoDaddy (incredibly confusing compared to other hosting providers). SO if you're skilled at migrating sites WITHIN GoDaddy and WITHIN the same account, and capable of explaining to me how to go about doing it all, PLEASE reach out! Honestly though, I'm looking to spend $10-$15 MAX for this. In general if everything was working well, it should take at most 5 minutes to make the necessary DNS changes, and then wait for the DNS to propagate. So if you genuinely understand this processes without any questions, explaining the one or two steps I'm missing shouldn't take more than a few minutes! :D ~Thank you, I'm looking for this to happen ASAP. It's 10:00am EST.. I'd love to get this going within the hour!