Fresh install? Keeping posts?

Just delete all the files from your wordpress folder except your wp-config.php file and .htaccess file then upload a copy of the newest version. Then finding a new theme that you like because most likely any old ones you have will not be compatible.

Is there any way to easily install a fresh copy of WordPress while keeping posts, comments, categories, users?

Just for the sake of future readers: NO, you cannot have a new install and keeping old content.
What you need is upgrade.

Can someone please confirm if what jeremyclark13 said will work?

Almost.
Read the Upgrade tutorial I linked to.

I have read the upgrade tutorial, but there is something I do not understand.

If I want a completely fresh install, absolutely the default version of 2.5.1, but I want to keep all my old posts, categories and users, should I overwrite /themes and /plugins?

The instructions say to keep those, but I would be happy to delete and reinstall if that will help me understand the problems I have been experiencing with image uploads.

Thanks

You can export your site into an xml file, then reinstall, etc (provided you don’t delete themes, plugins and uploads), but you may find your problems continue… I tried that myself, and all my posts, comments, etc. are safe, but nothing else seems to work… But that was why I deleted everything in the first place…

So in fact you CAN reinstall and keep your old content, it’s just a huge pain in the neck, and your site will probably never be exactly the same.

Thanks. That might be the way to go.