I believe your site was hacked or perhaps a piece of code was edited incorrectly.
If you view the source code on any page on your site you will see either before or after the body tag an image - that should not be there and it's likely killing your cookies (so you can't login). What you need to do so go through all of your 'index.php' file and look for the bad code (it's usually inserted to the end of the file) and remove it. It might be in more than one file...
There are some other threads around here with notes about cleaning up files if you search on 'hack'.
If you have a backup of your site already you could also easily restore. If not, backup your site before you do anything (even with the hack code in there)...clean things up...and then backup again.