The error message pretty much spells it out: something at line 2 of index.php is sending output to the client, which means that the session_start() at loine 14 of template.php cannot be executed. Note that "output" can simply be anything - including spaces or newlines - not within <?php ... ?> tags, besides obvious things like echo and print commands.
If it's still not obvious to you after looking at those files, then copy and paste at least the first part of each file for us to look at (at least through the line numbers mentioned in the error message).