I have seen instructions that say just that. However, there obviously is something missing as I have done just what you say.
Here is what I have done
1. Downloaded and unzipped the latest WordPress to my harddrive
2. Here is where there is a HUGE gap in the process. I have copied the existing wp-config.php and edited it so that $table_prefix = 'wp_'; does indeed have a different prefix. The prefix I edited to is wpna_
3. I left everything else in the wp-config.php the same. Copied the file back to the newly unzipped files in the correct folder.
4. Called the wp-admin/install.php file from the browser. However, get the following error:
Error establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can't contact the database server at XXXXXX. This could mean your host's database server is down. "XXXXX" being the current database name.
5. I have tried different Database Names in the wp-config.php file but continually get the same error.
What Database name is it looking for then if I am trying to use the same DB?
This is obviously not as simple as merely changing the $table_prefix