Classic ASP Connection to SQL Server 2014 without TLS 1.0 using ADODB.Connection
You might possibly be trying to use 32 bit legacy drivers. 

Try running C:\Windows\SysWOW64\odbcad32.exe to create a DSN that connects to your SQL Server database using the 32 bit SQL Server driver. First test the connectivity using the GUI.

Then try specifying your DSN in your connection string like so:

DSN=myDsn;Uid=myUsername;Pwd=;


The 64-bit version is located in:
C:\Windows\System32\odbcad32.exe

P.S. I've not tried this but the provider name for the 32-bit SQL Server is actually "SQL Server". It'd be nice if all you had to do was replace SQLNCLI11 with SQL Server. Here's my file DSN I created with the 32 bit version--notice the driver...

[ODBC]
DRIVER=SQL Server
UID=sa
WSID=P13-0000
APP=Microsoft® Windows® Operating System
SERVER=mcdba1