Unable to create a datasource. Datasource fails to ‘test successfully’ for SSRS

Depending on the version of Report Builder, you can only build from a single data source. I'm pretty sure this is still the case with SQL Server 2008R2, although Report Builder 3 can consume data directly from a database without needing a report model, although you need to build data sets using the individual connections and I don't think you can group items from different data sets by a common value.

You can do this gouping with SSRS (see this article for an overview), although I can't see an obvious way to do it in RB3. This article indicates that you can't nest items based on different data sets, so it's looking like common rollups aren't possible in RB3.

I found the solution in case anyone else comes across this.

The issue lied in the connection string property of the data source. For some reason (maybe standard, I am simply unaware of why) the connection string properties were empty after importing them to the new server. After setting them, they were able to hit the stored procedures and all reports ran as intended.