Hi Dave and welcome to the Magix user to user public forums.
If I were you, because the program is quite old in generational terms, I would go directly to the Magix site and choose the upgrade option there. Trying to get an internet connection via an old program that may not support newer internet protocols probably won't work. Or you could try contacting Magix directly with the sales@magix.net. email address.
. . . . Trying to upgrade my Movie Edit Pro 15 Plus. --> Online Update --> . . . .
Upgrading and updating are two different things. The update online is looking for patches for MEP 15.
To Upgrade, ie to get the latest version, is as @CubeAce has stated best if you contact Magix Sales as I suspect MEP 15 may be too old to qualify for the upgrade price.
Before upgrading ensure your computer specification is above the minimums required, especially if you intend working with 2.7K or higher resolution video, and Windows is version 8 or 10 and 64 bit.