In testing out our migrated V4 to v7 site, I see that the Authorize.net settings look correct. But every order that is placed is declined an gives a "Gateway Code" of 103 and a string "This transaction cannot be accepted.".

I also see no indication from the Authorize.net side that ANY transaction has taken place (usually I see some sort of transaction attempt logged).

What do I have to do to get Authorize.net to process orders without giving the 103?

I solved my own problem, so here is the solution for others with the same problem.

Gateway code 103 from Authorize.net means that the credentials sent with a transaction do not match (username, password or transaction key) the account. This was because my password in V7 had been put in the Transaction Key field during migration.

The V4 store passed the password for the Authorize.net account with each transaction. V7 passes the Transaction Key, which is different. During the migration, the Authorize.net setup had the password in place of the Transaction key. I changed the Transaction Key field to the transaction key and it now works.