You don't have to be a coder to use the self hosted version of WordPress, but it certainly helps if you're prepared to get your hands dirty and are willing to learn a bit about how it works in order to get the best out of it.
If you don't want to bother with any of that, or if you don't want the hassle of keeping it up to date or managing it, then the WordPress.com version is for you. It's ease of use vs a more customisable blogging solution.
Start by downloading a fresh copy of WordPress:
...and unzip it onto your hard drive.
Then grab your wp-config.php from your webspace and save it onto your hard drive as wp-config-hacked.php (or something). Close it.
Download another copy of the wp-config.php file and open it.
In the unzipped fresh version of WordPress you've now got on your hard drive, find and open the wp-config-sample.php file.
You should be able to fill in the relevant details on the wp-config-sample.php file, using the hacked wp-config.php file as your source. You should find the database username and password that you can insert (it goes in the "usernamehere" and the "yourpasswordhere" space).
Then you can fill in the four Authentication keys lines, using this page - just copy and paste them into your wp-config-sample.php in the relevant space:
Once you're done, save it as wp-config.php, then upload that to your webspace and see what happens.