Try downloading a separate copy of Firefox and run it from the folder(do not sign into you Firefox account) to see what happens.

https://www.mozilla.org/en-US/firefox/all/#product-desktop-release

Can you also post a screenshot showing the issue? Did you try safe mode?

Firefox safe mode: Click the menu button, click Help and select Restart with Add-ons Disabled…. Firefox will start up with the Firefox Safe Mode dialog.

Hello,

In order to better assist you with your issue please provide us with a screenshot. If you need help to create a screenshot, please see How do I create a screenshot of my problem?

Once you've done this, attach the saved screenshot file to your forum post by clicking the Browse... button below the Post your reply box. This will help us to visualize the problem.

Thank you!

Go to the Mozilla Add-ons Web Page {web Link} (There’s a lot of good stuff here) and search for a download manager.

This download manager works separately from the browser. The browser tells it what to download, and off it goes.

http://www.freedownloadmanager.org It is a powerful modern download accelerator and organizer for Windows and Mac.