When asking a question like that, it is best to include the following information (and anything else you think could be relevant):
Host operating system (or type of hosting)
MySQL version
PHP version
Previous Drupal Version
Modules installed
Theme being used (very important, as pointed out by someone here).
Always backup your old site completely (directories and database); if you have a hosting and are unsure about how to do a complete backup, get a complete backup of your hosting site.
Log in as user #1.
Did you try disabling all the modules first? And changing the theme to bluemarine? If you do that, and the update works, then you can gradually update the theme you use, and/or the modules, and find out what the problem is!
With more information, the good folks here on the support list (mucha experiencia!) can try to guess what is wrong.