Do you know how to build a GUI using Matlab that take in "username" and "password"?
The system have to ensure that the password is correct in order for the user to proceed.

There is a lot of information on the Matlab website on creating GUIs. If your application is simple without the need for any serious security, you should be able to simply compare the entered password with a saved one.

Start here with these resources

This link from the file-exchange should help you
http://blogs.mathworks.com/pick/2007/10/05/masking-typed-passwords-with-asterisks/

Of course, if your application has more than one legal user, you probably will also need to hard-code more than one password. And things do get tricky when the number of potential users is not known at the time you release the application...

A feasible alternative in this case is to go for license keys which embed user/corporate information in encrypted format. The application should parse the license key before starting and launch only if a valid license key is found. This is what is normally done on MS Windows applications, and the approach also facilitates limited duration license keys and hardware locking (whereby application execution is forbidden on other computers to prevent unlicensed distribution).

There is a range of examples of various possibilities in relation to the above downloadable at http://www.algorithmprotection.com