"Cannot redeclare i18n_variable_set()"
The issue here appears to be that you have installed the same module in two directories:

sites/all/modules/contrib/i18n


and

sites/all/modules/i18n


and drupal is picking them both up.  If this is the case, I would disable the module, uninstall it, delete one of the directories above, and then re-enable the module.  That should clear this up.

If you can't access your site's admin UI at all, then you will have to go in and remove one of the directories directly; I would suggest removing sites/all/modules/i18n as the other directory appears to be being searched first.

ADDITION:  From some line number searching, the Drupal 6 version of i18n.module declares i18n_variable_set() from lines 881 to 894 and the Drupal 7 version doesn't even get that long--ending at line 610.  This coupled with the fact that the i18n_variable submodule isn't even included with the Drupal 6 version has me thinking you have a sorts of module mish mash going on here.

ADDITION 2:

I just installed the Drupal 7 i18n module on a clean install in:

sites/all/modules/i18n


and enabled it and the i18n variable module.  ALL good.

I then copied the Drupal 6 i18n module's code into:

sites/all/modules/contrib/i18n


and....


  PHP Fatal error:  Cannot redeclare i18n_variable_set() (previously declared in /Applications/MAMP/htdocs/d7lrfm/sites/all/modules/i18n/i18n_variable/i18n_variable.module:116) in /Applications/MAMP/htdocs/d7lrfm/sites/all/modules/contrib/i18n/i18n.module on line 894


so, I would check to see if the same thing is happening on your site and if so, remove the errant Drupal 6 version.  A quick check of the .info files will show you what core version of Drupal they are for.  (And, oops, yes, here I put the Drupal 6 version in sites/all/modules/contrib/i18n and the Drupal 7 one in sites/all/modules/i18n which appears to be opposite of what's happening on your site, but I tried to be as similar as possible :)