Depends on how many databases your hosting plan allows. Sounds like you may be limited to just one. That information_schema database is the database that stores info about all the other databases, so don't delete that!
You want to EXPORT to a *.sql file. So if you are in PHPMyAdmin and can see the two databases, click on the benmeyer database. You should be able to then click on Export Tab on the right side of the screen. Then make sure all the tables are selected (Select All); make sure that the radio button says SQL. On the right column, check Drop Tables. Then scroll down and check Save as File. You don't have to populate it with anything, PHPMyAdmin will do this for you. Then you should be able to save the *.sql file (which is just a text file) to your hard drive.
Congratulations, you've just backed up your database. With that out of the way, you should be able to do a reinstall. If something goes wrong, you have your backup copy there. Good luck!
Oh, if you just want to backup your posts and pages, what you can do instead is export a table from the database, not the whole database. In that case, you'd click on the table "posts" and do the same thing as I've outlined above, except that instead of exporting (backing up) the entire database, you've just exported the table that contains your WordPress pages and posts. Bear in mind that if you decide to take this "scorched earth" route and do a clean install of WP and then import that table into the freshly created database, you'll have to reconfigure everything else. This will just preserve your posts and pages.
bencmeyer
