Our free Magento extension can automatically generate API credentials for you. See it's step-by-step guide here.
If for any reason you wish to generate the API credentials by your self, please use this guide here and/or this video tutorial.
If the API credentials still don't work for you, please provide us with the following screenshots:
1. List of users - System > WebServices > Users
2. Users Roles - System > WebServices > Users > Click on user > User Role (from left side)
3. Role Resources - System > WebServices > Roles > Click on role > Role Users