That seems more of an installation problem to me, especially the fact that the warning is about a "non-existent class" and inability to open a php file.  The process I described is a normal part of the admin interface that should work perfectly well, I simply "discovered" that it could solve my particular problem.

Besides, disabling cache doesn't bring any changes to the frontpage.

I wouldn't expect any change in the frontpage just because you disable the cache.  In my particular case I have a website that automatically aggregates news articles from other sites, without human intervention.  That means new articles are written directly into the DB without any frontend or backend action, which as I understand is necessary for JRE cache to realize that it must delete a certain cache file (the frontpage cache file for example) - that's the reason why my frontpage stayed constant even when there were new articles in the DB.  If you capture your articles manually then you don't need to disable cache of the front page if you keep JRE's default settings, because your very action of saving a new article will tell JRE to renew.
cheers

I found it!
I'll answer here to myself in case it's useful to someone else: just enter the cache repository overview and click the green icon that says "may cache" - the green icon will be replaced with an X, and the frontpage (or any other url for that matter) won't be cached anymore 

just did per your recommendation, but doesn't work 
is that supposed to work?

The component works great, but I simply can't take my front page out of the cache.  I've already tried putting "/" in the section for entering URL parts that may not be cached, but then it doesn't cache anything.  Any ideas? "/" is how the front page appears in the repository. 

I am trying to buy your Joomla Cache accelerate component right now from the US for a site based in Mexico.  From your comments here I understand that I can buy it tax free, but I can't find a way to do it.  Can you please tell me how?

What are the advantages of this component over the free GNU/GPL Ircmaxell's Page Cache?

cool, where do I send it? it's just a regular template with some additions that I don't want to lose.

Before buying - I have made several changes to my index.php file, and I need those changes to stay there.  Given that installing the accelerate component patches the index.php file, how can I make sure my customizations will stay there?

Can I program at what time -or in what minute of each hour- I want the cache to expire? the main reason I want this component is because my server updates its content every half hour, and the process takes one or two minutes in which the server is down.  I want to program the component so that the cache is always on during the updating process, and then set the cache to expire when the server isn't busy anymore.  Is it possible to do this and to program for example the cache to expire on the 15th and 45th minute of every hour? or is it random at fixed intervals depending on the minute in which it started?

Before buying, I run a news site (http://www.mexicolibre.com.mx) and want some of the pages to have a short-lived cache (such as the politics or sports section for example) and some of the pages to have a very long-lived cache (such as the articles themselves, which are rarely edited).  I don't want to completely disable the cache from the section pages because they are the most highly visited and where I need it the most, and I don't want to give a short-lived cache to articles, is this possible?