I have created a C++ dll. It works fine and does the job.
I have created methods in asp.net that call the methods in C++ dll. DLL path is absolute. It works fine to
Did you confirm that the authenticated user of the application pool which is running your app has the appropriate permissions to read and execute the DLL?
Try adding permissions for the user who is running the application pool for IIS7. For IIS6, if you are using anonymous authentication trying giving permission to the IIS anonymous user as configured in your Web Site settings. See here for IIS6 and here for IIS7.