I think your problem is
jQuery UI, not
jQuery. jQuery will only be a problem for you if your WordPress version is outdated.
If your current WP install loads
jQuery 1.4.2 & above, you only might need to change
jQuery UI related files.
In your code:
wp_register_script( 'jquery', 'http://accesototalpuebla.com/accesototal/wp-content/plugins/nextgen-gallery/js/jquery.cycle.all.min.js?ver=2.88');
You are loading up
jquery.cycle.all.min which is NOT jQuery. WordPress uses the internal handle 'jquery' to load the jQuery library (not any of the jQuery Plugins)
WordPress currently uses a jQuery UI that is (I think) version 1.7.3.
If I'm not mistaken, nextGEN requires jQuery UI 1.8.6 because it has a new auto-complete feature that is only available in jQuery UI's 1.8X versions.
So what I think is happening is that WordPress (or a plugin you installed) might already be loading WP's internal jQuery UI 1.7.3 files which is conflicting with nextGEN's 1.8.6 version. (You can't load both versions at the same time).
An important point to note is that de-registering jQuery UI is not as simple as
From the best of my knowledge, WP loads individual elements (various files) of the library. You can scroll down the page (the link I posted above) to see a reference to all of WP's jquery-ui components and their handles.
You have to check if these are used (that they are loaded up). You can do that by using Firefox with Firebug or Chrome's developer console to see what resources are loaded when the page loads.
You also really ought to try and understand the whole codex page that I linked to earlier. That way, you'll understand what went wrong with your code above.
The only reason I think it might be jQuery UI is because it happened to me when I was creating a plugin. I had the exact same error as you did.
I wish you the best in debugging you code.