Hello, I need to build a brand new custom moodle 1.9 theme. I have failed to create a moodle 1.9 website that functions. Should I choose to develop a new theme in the latest version of moodle, will it be compatible with moodle 1.9? Alternatively, can someone suggest how I might easily create a moodle 1.9 environment?
Moodle 2.9 themes are not at all compatible with Moodle 1.9.
You probably don't have much control over the situation, but Moodle 1.9 is now completely unsupported - no bug fixes, no security fixes and (in pretty much all cases) no fixes from 3rd-part plugin developers to support it. The first thing that should happen is for the site you are working with to upgrade to Moodle 2.9 (via Moodle 2.2).
As for setting up Moodle 1.9, it should be more or less the same as setting up a Moodle 2.9 site. As a quick experiment, I just tried an install based on some M1.9 code I had lying around and it worked fine, apart from a few debugging warnings, on the same dev box I've got all my other Moodle sites on (in case it helps: Debian Linux + Apache webserver + PHP 5.6 + MySQL 5.5.44).
Not only did themes change entirely between Moodle1.9 and Moodle2.0 but they have been constantly developing and improving with every version since then. So no, as Davo says, you cannot create a 1.9 theme on Moodle2.x
You can set up 1.9 in the same way as 2.x on a local computer to develop a theme. You may then be able to find some useful themes in the OLD themes list https://moodle.org/mod/data/view.php?id=6552 and old 1.9 themes documentation at https://docs.moodle.org/dev/Themes_1.9
However, please bear in mind that both Moodle1.9 and its themes are unsupported and the best solution to your issue, as Davo suggests, would be to get the site upgraded - both for the sake of the features, the support and also the security fixes that have gone on over the last few years.