There are many threads attempting to assist users with new installs of WordPress on "localhost" utilizing the Xampp service that seem to lead everyone into speculative circles with no solution. Fortunately, having had some difficulty myself and getting very frustrated, I finally resolved my issue and have the solution available for others.
To begin, download and install Xampp as per the instructions found on "Geeks are Sexy". I personally disabled my antivirus and windows firewall prior to install.
When editing your 'wp-config.php' file as described in the tutorial, be sure to select the yourpasswordhere part of the define ('DB_PASSWORD', 'yourpasswordhere'); // ...and password portion. Once you have selected it, delete it (if you are following the instructions verbatim). Do not use a space or delete the two apostrophes on either side of "yourpasswordhere" as it will cause you to get the error of unable to connect to database.
Happy blogging to all.