This will be caused by Transaction Broker trying to connect to the Dimensions database using an ODBC connection that does not exist/has been renamed.
To fix the connection:
Within Transaction Broker, click Transaction Broker
Click Define Datalinks
Select the datalink you're trying to process, and click the Edit icon
At the bottom of this screen is the connection to Dimensions. In the Data Source Name field, clear the existing data source and then click the Magnifying Glass icon.
Select from this list the data source used to connect to Dimensions. There is usually only 1 connection in this list, but if you're unsure you can do the following:
Open Dimensions, at the login screen, click More > >. Note down the ODBC Link used here, and select this in step 5 above.
When that has been selected, on the right, click OK to test the connection, this should now come back successful.
Click Save and the top left to save the changes.