There's no point in cutting up a 7mb file. Youd do that for a file in the hundreds of megabytes. If you're getting an error with phpmyadmin, the next easiest way will be to upload the file and run the command from the shell.
This Wiki article should be of some help. But here's the basics.
1) log into FTP. Upload the backup.sql file, just drop it into that first folder you get when you log into FTP. That's your home folder.
2) next you're going to log into ssh. You'll have to use a program like hyper terminal in windows or a program called putty. You have to log into ssh or telnet (same thing) with a user/pass that has shell access. You can check this in the Panel > Users > Manage Users > Edit.
3) Now you'll need to type in the command to dump your database. This is where that wiki article or the k-base will come in handy. Look there for the command to type. Just remember to update the relevant parts like your database info and the user/pass.
Becuase you uploaded the to your home directory, when you type that command, you don't have to worry about giving it a direcotry path to your file. Let me know if somethign isn't making sense.