Two problems on a custom site: - unremovable notice on front page and wrong logo link

It sounds like you have a custom Drupal theme in which some stuff has been hardcoded so that you can't see it in the usual Drupal Administration screens.

the front page says you can't access site or something to that effect

Try looking at Administration > Site information and then at the bottom of the page, where it says Default front page. Does the box there have "node" filled in? Or something else?

If it does just have "node," maybe there is a custom front-page template. On your server, look in the folder of the theme that's currently active on your site. Is there a file called "page-front.tpl.php"? If so, that's a custom front page template. Try renaming it to "page-front.tpl.php.bak", clearing your cache, and reloading your site in your browser. (If it doesn't work, rename that file back to "page-front.tpl.php".)

If it doesn't just have "node," but instead has "node/17" or something like that, someone set the front page to be a different node. You can either set it back to "node" to make it more like a default Drupal site, or you can create a new page that does what you want (let's say it's called "node/28") and then put that in the Default front page slot instead.

the site name is directed to a domain that i do not have any more so i was wondering how i can redirect it to the domain that i do have!

If I'm understanding this correctly, let's say your site is http://www.cats.org and it used to be http://www.dogs.org. If you click on the name of your site in the header of any page, it still takes you to http://www.dogs.org?

Take a look, again on the server, at "page.tpl.php", which is the basic page template for your site. In the code for the header, do you see something like this? Look for "print $site_name" especially:

<span class="titleheader"><?php if ($site_name) { ?><h1><a href="<?php print $base_path ?>" title="<?php print t('Home') ?>" id="header"><?php print $site_name ?></a></h1><?php } ?></span>

$basepath is what Drupal thinks is the base URL of your site is. Instead of using that variable, has somebody put a literal link like this: <a href="http://www.dogs.org"><?php print $site_name ?></a>?

If it does use $basepath, then I think we've come to the end of my Drupal knowledge, and maybe someone else can help.