Could you point what configuration is probably preventing a Laravel site to work in web?

You are not providing a lot of information.

1. Does it work on localhost?
2. What happens on the ISP's server?
3. Providing a link to the site on the web may be a great help.

Hi

Here it is:

1. Yes, it runs localhost.
2.

3.
http://www.espiriplug.com.br/aplicacao-cliente/

In the meanwhile I change something

Introduce .htaccess   and  index.php  at the project folder

Ok, let's walk before we run:

For this test, all you require in .htaccess is

DirectoryIndex index.php

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For a Laravel app, you would normally have

<IfModule mod_rewrite.c>
    <IfModule mod_negotiation.c>
        Options -MultiViews
    </IfModule>

    RewriteEngine On

    # Redirect Trailing Slashes If Not A Folder...
    RewriteCond %{REQUEST_FILENAME} !-d
    RewriteRule ^(.*)/$ /$1 [L,R=301]

    # Handle Front Controller...
    RewriteCond %{REQUEST_FILENAME} !-d
    RewriteCond %{REQUEST_FILENAME} !-f
    RewriteRule ^ index.php [L]

    # Handle Authorization Header
    RewriteCond %{HTTP:Authorization} .
    RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
</IfModule>

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To check if your web hosting setup is OK, create an index.php file exactly as follows:

<?php
phpinfo();

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and nothing else.

Visit the URL and you should see your PHP config. If you don't, your web hosting setup is wrong.

Try that, and then we can go to the next step.

Hi

I eliminated the index.php at the app root

In the app root  .htaccess  just put:

DirectoryIndex index.php

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Hostig is OK;

The result is a blank page.

You are confusing me - the result looks like the PHP config, not a blank page.

Sorry.

What I mean is
1. The hosting is OK, accordingly with the php info image above.

2. Configuring  .htaccess  at the application folder with

DirectoryIndex index.php

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Eliminating the app root's   index.php

Eliminating the app root's   .htaccess

(Maintainig only the default index.php that is at Laravel's public folder)

The result is a blank page.

Mistake:
Eliminating the app root's   .htaccess

Correct:
Eliminating the public folder   .htaccess

(accordingly with the picture)

I read.

I don't know if correctly understand,

If I have Codeigniter and pure PHP... in this site, a Laravel app could cohabit independently?

Hi

Since the subject derivated from the original purpose of the question I openned another question:

https://www.experts-exchange.com/questions/28954724/Could-you-explain-how-to-create-a-Linux-virtual-server-to-use-Laravel-on-the-WEB.html

You could test out Laravel website with dedicated servers where you get staging url instead of shared server. Try out any laravel hosting provider that provides staging url. You can deploy your site there with git or sftp and test the site out.