Page Redirects locked out of wp-admin

Let me preface this by saying every solution previously offered in the support forums for this problem has been attempted without success.

Trying to access the backend of my WP install using the suffix /wp-admin I get a redirect to a 404 page.
http://mexicotrucker.com/wp-login.php?redirect_to=http%3A%2F%2Fmexicotrucker.com%2Fwp-admin%2F&reauth=1

When I try to access it with the suffix /wp-login it will go to an error page within whatever browser I am using and advise “This page has Redirects”….

Other times it will come back with a Fatal Error out of memory etc. despite having increased memory size to 512 or above

I have reinstalled via FTP a fresh instance of wp-admin and wp-include directories after deleting the original

I have tried accessing the admin screen after disabling .htaccess and the plugins directory as suggested in several threads on this support forum

The site itself seems to come up fine at Mexico Trucker Online but attempts to access parts of the site throw errors.

My host claims that it is a problem within WordPress, not something on their servers.

After browsing the forums the entire night, I’m out of ideas.

Can anyone help me out here?

Thanks