How to alter my search

I currently has a large directory website setup at Greenbookpages.com. This theme comes with search capabilities but only searches post content and post title for search results.

I would love if I could alter this search so it would also search category. For example if I type the name of a category into the search all posts under that category are displayed. I still wish for the search to search post title and content but also categories. Make sense?

Here is the coding for my search, is there something I can add to have it search categories? Would this be a simple task or take alot of coding?

[Code moderated as per the Forum Rules. Please use the pastebin]

[No bumping, please.]