Databases on localhost

I have installed two wordpress sites on my local machine for test and developement purposes. Everthing worked well under the original install. Now, I want to take the database from one site and rename it and make it so that the other site uses it. I have tried downloading the database and importing it into the other database but with no luck. In the wp-config.php file, I changed the database name that is being looked for and the database prefix all to no avail. I’m sure that this is a simple fix and I am not seeing something but after trying to work through it for the past two days, it is time to cry “Uncle” and ask for your help.