I would think that the plugin is still running and inserting the code in the pages even though you have it deactivated. I surely hope the plugin didn’t edit your page templates directly and insert its code. If it did that, then you will need to manually remove the code from the page templates of your theme (index.php, page.php, single.php, etc.) or restore the page templates from a backup to removed the code.
Usually plugins insert their code into the page on the fly when the person visiting the site requests the web page. They shouldn’t permanently add their code into your theme’s template files.
I know you mentioned web browser cache above, but do you by any chance have the WP Super Cache or W3 Total Cache plugin running on your website? If yes, the you need to clear their cache via their area under the WordPress Dashboard to remove the plugins code from the pages being server to people. I am guessing you are not using something like a CDN (content delivery network), but if you are, then you may need to clear that services cache also to clear up this problem.
I am guessing the solution to this problem is to remove the plugin via FTP. If something goes wrong, then you should be able to add the plugin again via FTP by uploading its directory to the “wp-content/plugins” directory and everything should be back again, but unfortunately you will still be stuck with its code in your theme templates.
I guess another option would be to delete your theme’s directory under “wp-content/themes” after making a backup and upload a fresh copy of it and see if that clears things up if nothing else works.