Is there a way to "hard-reset" a module? I'm not sure why, but I am having extreme problems with several modules, but most noticeably, the signup module. The problems that I am having are sudden, and were not there yesterday, so I know it isn't a problem with the design of the module. I have tried patches, but those have caused other problems. Then it occurred to me: why should I have to do anything like that? Shouldn't there be a way to "hard-reset" a module? (ie remove the module and any remnance of it from the drupal database, and start from scratch as if the module was never installed in the first place, and then go and reinstall it) I have tried uninstalling it, deleting the module files, and the re downloading it and enabling it, but I get the same errors when I enable it again. How can I be delete it as if it was never there to begin with so I can start with a clean slate?
This answer reflects my understanding of how Drupal is working.  Anyone with more or different understanding, please speak up, I'd love to know more.

Removing all remnants of a module by uninstalling it works only as well as the code included by the module for cleaning up after itself.  For instance, if it has made a change such as adding tables or otherwise changing the database and does not properly delete the tables, they will remain  there.  Removing the module, should remove much of its potential to cause a problem provided that Drupal core knows it is gone and does not hang up looking for hooks that the module provided.  Have you run 'update.php' in the URL?  This will cause Drupal to update all the connections to the module.  If the module is gone, then it won't make calls to it that cannot be responded to.

The only way to really reset Drupal is to maintain backups.  Make backups before installing any module and at least every day or so during site development. The module Backup and Migrate is a simple way to simplify  site database backups. In addition, it is also a good idea to look into using Git to keep track of your code when developing a site.  Git is basically a unix tool, but there are windows UI versions such as GitGui that are not difficult to learn and put to work keeping track opf your code.