Bottom line ... no way ... unless you have a test server of your own (localhost VirtualBox with X Guest OS) that you could dummy down the versions of PHP and MySQL to compat versions just to do old hops. Trouble with that is ... where would you acquire the old versions of PHP and MySQL (probably Apache also)? Makers of those do have an archive of old versions for download. Do a google search for PHP 5.1.x or MySQL 5.0.28:
I'll save you some time:
You'll be scrolling down a long time before you find 5.1.x.
If you note, old versions are available as .tar.gz's **but** may not include all the PHP extensions to run a Moodle! :| See attached text file for how to build extensions.
For MySQL, it's even more complicated:
So, in that light, there is but one saving grace to your situation ... in your moodledata directory you will find numbered directories. Those numbers are the course ID's. Inside those #'d directories, you will find a file directory and inside that, files you have uploaded to those courses by humanly recognizable names (the last time moodle did that was the highest of 1.9 which was .20 if I re-call correctly).
So you could download your moodledata directory, and sort through all those files saving them to some local re-construction of course names.
Then, install a fresh 3.9.highest on a server, rebuild categories of courses to mimic oldsite, start a new fresh course that is named the same as old 1.6.x or 1.8.x course, and rebuild the course. You have at least the files used in the old course(s).
That is probably the path of least resistance.
Of course any true Moodle guru age 70 or older could argue above and they might have nothing else to do and have all the time in the world (yeah, right) to set up a local VirtualBox server and play for hours and hours to march ... and it would be a march ... a total site backup of what you have,upwards ... painfully ... and with hickups along the road (NO yellow brick!).
Uhhh .... any test site with those old versions on internet would be prime target for take over ... so while one was marching, one would also have to fend off those that would be trying to use your server for other purposes. Don't think any provider would tolerate that very long once discovered ... and there is no doubt a server like that would be discovered. That's why I suggested VirtualBox with an OLD OS on your local machine.