Do you still have the config.php file from the 1.9.older Moodle that was installed by some script the hosting provider grants permissions to use to shared customers?
In the config.php file there is a path to the moodledata folder. Take a look at that path. In a new install, path should be similar. What is that path?
So sounds like the provider creates a cgi-bin directory for you when the account is established. Would think that it has 'special' settings still and am really surprised that your previous install worked with moodledata in cgi-bin. To me, that's kinda scary ... cgi-bin is normally open to outside access and if one tinkered with the URL link a little am pretty sure one could actually see/browse your moodledata directory (unless you took some preventative measures) ... uhhhh, not good.
When moving upwards code wise, best not to attempt to overwrite files/folders ... fresh code is safer. ** keep a copy of the config.php file **
As far as approaching the next step to a 2.x - first things first. If one can't get an upgrade to the current 1.9 version sorted out, then 2 will have issues as well.
Sigh ... one button upgrades ... yes, would be nice. WordPress has it (within a series), Joomla 2.6+ has it (within a series), but neither of those can be upgraded to the next version (ie, out of series).
What you are doing is NOT within a series ... it's 1.9.x to 2.x (whatever you can run with current hosting provider restrictions). It is a complete re-write of code.
Shared systems are cheap for a reason!
'spirit of sharing', Ken