in reply to @ISA not behaving in OO test

First of all I should mention that <code>...</code> tags make it easier for people to download and try your code out.

Anyways if you did a:

use diagnostics;
you would get the information that you were trying to put a package in @ISA that doesn't seem to exist. Which is (from Perl's point of view) exactly what is going on. Nowhere do you load Banach/Web/t.pm, and so that namespace is not in use. Just slip:
use Banach::Web::t;
into Banach/Web/s.pm and your problems should go away.

An incidental hint. If you are developing code you should probably not work directly in your installed directory. Instead look into using the lib pragma.