The Firefox 3.6 download is instead installing version 220.127.116.11
I am attempting to install the latest version of Firefox 3.6 from this site: http://www.mozilla.com/en-US/firefox/ using the Firefox 3.6 Free Download link; however, when the install finishes and Firefox launches, when I go to the Help>About menu to check the current version, the bottom of the window says I have installed "Mozilla/5.0 (Windows; U; Windows NT 6.0; en-US; rv:18.104.22.168; .NET CLR 3.0; ffco7) Gecko/20080404 Firefox/22.214.171.124". As you may have noted, that indicates the current version of Firefox is 126.96.36.199 and -not- 3.6.13 (or whatever the most recent version is). Is this just a bad registry entry or other taint from a previous install, or is the file that I am downloading and installing (named "Firefox Setup 3.6.13.exe") not the correct one? If the former, then what steps should I take to troubleshoot/remedy this? If the latter, then is there some way I can get the correct file to install 3.6.13 or the latest version?
Your UserAgent string in Firefox is messed up by another program or addon that you installed. Probably related to that ffco7 in the UA string.
type about:config in the URL bar and hit Enter
If you see the warning, you can confirm that you want to access that page.
Filter = general.useragent.
Right-click every preference that is "userset" and in bold type, one line at a time, and select Reset.
Then restart Firefox
Your above posted system details show multiple Java Console extensions.
You can uninstall (remove) the Java Console extensions, you do not need them to run Java applets.