First, remove the user.js file. Firefox reads this file at startup and uses it to override your previous session settings. This article describes how to locate the file: How to fix preferences that won't save.

Second, run the Search Reset extension to fix your home page and new tab pages back to their defaults:

https://addons.mozilla.org/firefox/addon/searchreset/

If the problem recurs, one of your extensions could be the problem. Try this:

Disable ALL nonessential or unrecognized extensions on the Add-ons page. Either:

• Ctrl+Shift+a
• orange Firefox button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Usually a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Can you completely get rid of it?

I also think that although your anti-malware efforts may have removed numerous items, it's worth a visit to the Windows Control Panel, Uninstall a Program. Clicking the "Installed on" column heading helps in seeing what items were bundled together, in case their names are not obvious.

I associate Conduit with various "Community Toolbar" products.