Well, to find out wether the stumbling block is Perl, ODBC, some driver or even the database configuration, I'd try to connect to the database via the most simple tool. "Simple" in this case means: pre-existing and easily configured. If you're on Windows, you might have MS Access or Excel, both of which can connect to "external" sources, hidden under something like "Import external data".
There probably is the possibility to use native MSSQL. I'd try this first to see if the database is reachable at all.
I know cygwin Perl only from hearsay, but chances are that instead of DBD::ODBC you could also use DBD::ADO (I use this with Strawberry Perl), which AFAIK uses the same "native" drivers as Excel/Access.
Then I'd try ODBC (probably under "other", where you will have to select in a next step some "data source". If it is not already set up for you, you'll need it for Perl, too, anyway.
After you got that working, you can extract the connection string from the connection's properties within Excel/Access
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