Hi,
Yes, you can migrate your old database to a new install of WordPress. There are a couple ways to do it, both of which can use the .sql file.
First, if you have access to PHPMyAdmin:
1. Click on the database on the far left. It will have a title corresponding to the new WordPress install.
2. About halfway down the page, click "check all" so that all tables are selected. Then, select "drop" from the dropdown menu.
Something to note about PHPMyAdmin. There is a size limit on databases, and this differs from host to host. Commonly, it is 8MB, and if the file is bigger than that, then the import will fail. It depends on the host whether or not they will either up this limit temporarily, or do the import for you, or whether you will have to do this through the shell, assuming you have that access.
3. Click "yes" to confirm.
4. Click the "import" tab.
6. Click "choose file".
7. Find the database file (the .sql file).
8. click go, located at the bottom of the page.
There is an article on the Codex entitled "Moving WordPress" that will provide more info should you have to use shell to do the import.
Hope this helps,
Amanda