Not the library, the actual data files. Depending on IIS version you are into Kerebos, NTLM, etc, and only with IE. Basically MS have it set up that IIS works with ASP and IE on an Intranet and is a pig to anyone else. The problem is that even though you have Mysql set up to run as a Windows user of some sort, IIS automatically works as an anonymous user with no windows authentication going on, except on an Intranet where you can use Integrated Windows Authentication.
Find your mysql data files directory in Windows Explorer and open them up to the world by right-click the directory->properties->security tab->advanced and add EVERYONE with Full Control, make sure you check 'apply to subfolders and files'