I'm missing my core search module I'm running Drupal 7.12 and had to build a module that extends the search functions of the core Search Module. I made the module, installed it in my custom module folder and reloaded my Drupal site only to find that the search bar couldn't be found on the page...

I looked through the module selector on my dashboard and looked through the core modules. Surprisingly, there was no search module listed in the core module section, although my module did show up in my custom module section (which is irrelevant because the module I wrote needs the core search engine to work).

I checked through my Drupal on my FTP site and found that the files for the core search module are still there.

Why isn't it appearing in my dashboard core module list, and how do I get my Drupal site to recognize that the files are still there?
I'd guess that your custom module is called search, which would conflict with the core Search module, also named search.

There's no such thing as namespaces with regards to Drupal modules (at least out of the box, I'm not sure if there are any contrib modules that deal with this. My gut instinct is that there wouldn't be). Each module needs to be individually named, or the last module of the same name that Drupal comes across will be the one it uses.

Make sure your module is not called search; that includes making sure the folder name for the module, the name of the .info file, name of .module file, etc. are not called search.info etc. That should make sure that both modules are available in your module list.