Login keeps kicking back

I recently installed WP on a client’s server and started working on the site. First time I went back to the site I had a couple of problems logging in, but it eventually went through. Now, i can’t get in at all. Every time I put the correct details in it kicks back to the login page. I have searched for a solution and tried everything I could find, but no success. We also wrote to the hosting company to see if was a server or database problem, and they say everything is functioning just fine. Here is a list of the things I tried before coming here:

-Entering wrong password and it tells me password is incorrect, so that is working, but with correct password, just kicks me back (no indication of password being incorrect).
-Have changed the password in the database using MD5 encryption, does the same thing.
-Tried resetting password through the “Lost your password” link, but get the following error:
“The e-mail could not be sent.
Possible reason: your host may have disabled the mail() function…” [they tested this and reported it operational]
-Tried registering a new account – says an email was sent, but no email received.
-I have changed the plugin folder name to plugins.old to disable all plugins, still doesn’t get past the login screen.
-Used different browsers, same problem.

If you would like to see for yourself, please go to http://celticpendants.co.uk/wp-admin with user: admin and pass: celticpass

Short of deleting everything and doing a complete new install, I am at whits end.

Thanks,
Lee