I am not sure if I agree with Ladydeluna. The headers are already sent, of course, since they are sent before the errors reach you via your browser [ie. WordPress database error: [Unknown column ‘none’ in ‘field list’]
INSERT INTO wp_post2cat (post_id, category_id) VALUES (87, none)]
You shouldn’t worry about this. What you should do is fall back to your original theme and turn off the shopping cart. If everything works then you won’t have to re-install WordPress – unless you have overwritten some of the files.
Like Ladydeluna says, disable your plugins and fall back to your original working theme. Everything works? Turn the plugin on. Still working? Try your theme.