I realize you're simply writing what you observe, but there's simply no connection between changing a CF Admin DSN to point to a new server, and a failure of a page reporting application pool problems. There must be some other explanation for your application error. Are you 100% positive that before you changed the DSN, the exact same URL from the exact same browser had been working? I'd think your application would fail with this error REGARDLESS of the change of the CF Admin DSN name used by that app.
Or here's a possibility: could it be that your application is now failing (because in changing the DSN, you have code still looking for the old DSN), and an error handler (either in CF or in IIS) may be redirecting requests to some new domain or folder, which may be different from the one you started the request on? Look closely to see if that URL is indeed changing.
Let us know what you find (or if you already found and solved this).
(And I would swear I offered this answer in days past, but I see it's not here.)