Are you sure you are not logged in? Have you tried clicking the home link in the breadcrumb?
Are you accessing more than one Moodle site from that computer? Does each site has a different cookie prefix set?
I have an instance of Moodle 1.9 running with PHP 5.3.10 and I do not see those errors in my logs. All ereg functions were indeed deprecated in PHP 5.3, but maybe some PHP builds have different warning settings. However, those warnings should not affect operation.
Installing and upgrading help
Can't login - Redirects but fails to login
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