I think you're right. After some more tracing, it seems my server process actually launches but the first thing it does is make an dbi::ODBC database connection attempt, which fails. So, arg I'm dumb.
FWIW, the IIS worker processes seem to run under the user "NETWORK SERVICE". I wonder if I just need to get my SQL Server to allow that user to connect/login.
I am running into this same exact problem but were having issues attempting to set up the connection including NETWORK SERVICES as a user in ODBC Data Sources.