When you reinstalled the extension, it might not have included the search plugin that adds a new service to the search box. Have you exited and restarted Firefox to see whether it shows up after a second restart?

If you cannot get it from another source, the plugin might still be saved in the "Old Firefox Data" folder that the Reset feature should have deposited in your desktop.

If you open that folder and then double-click into the searchplugins folder, can you see a file that looks like it would search answers.com? If so, you could try copying and pasting it into you current "live" searchplugins folder, then restart Firefox to see whether it is detected.

From within Firefox,

Help > Troubleshooting Information > "Show Folder" button

This should open your current Firefox settings (Firefox Profile) folder.

Keeping that folder open, switch back to Firefox and Exit

Pause while Firefox finishes its cleanup.

Is there a searchplugins folder? If so, double-click into that folder, then copy and paste the missing file from your old folder to your new one.

If there isn't a searchplugins folder, you could create one, or you could copy your entire old searchplugins folder to your new profile folder.

When you restart Firefox, did it detect and add the missing search engine?

Doh! Here's the easy way. Go to the following page, then click the icon at the left end of the search bar, and look for Add "Answers.com" on the drop-down menu.

http://www.answers.com/main/firefox_plugins.jsp

Does that work?