The error message is about MySQL, not mod_rewrite.

Check engine/settings.php and correct the database details there. You probably mistyped them during your initial setup.

Hello Kevin I have the same error.  I verify again and again and still with this error  :P

Just to know, elgg will work if mod_rewite doesnt't be working?

That's a database error as Kevin said.

Yes, Elgg requires mod_rewrite