Finding out template I'm working on this web site which I need to make changes to the heading part and I need to know which template or file is generating it so that I can add a slogan. My first attempt was using theme developer. However, it crashed the site so I had to disable it. Is there any other way I can track down the responsible template?  

Drupal 7.0
You are looking for Theme developer module:


  Firebug for Drupal themeing. See the screenshot and screencast. Note that this module injects markers into the DOM to do its magic. This may cause some themes to behave erratically and less capable browsers may make it worse (especially IE)/. Enable it when needed, and disable it afterwards. 






If it is crashing your website

You need to upgrade. You are at 7.0, current version is 7.31. You are 31 minor versions behind. And some of them was security updates. So you probably should upgrade anyway.