You could use a TV, and edit it with each document with the ID you want to use for the root of that document’s menu, and use the TV in the snippet call:
[[DropMenu?startDoc=`[*SubID*]`]]
However, this would mean you would have to edit this TV for every page. (a TV can be modified on a page-by-page basis, a very useful feature). Actually, the TV could be written to produce a drop-down list based on root-level document IDs, and then you would just select the the one you want, but still, you’d have to do it with each and every document.
There are two other methods, however.
I have a snippet that returns the "ultimate parent" (I just updated it). However, the way the DropMenu snippet is written, there is no way to tell it to not do a menu at all. I could hack it with a one-liner that would cause it to simply abort if it’s passed a value of -1 for the startDoc, and my ultimate parent snippet would return -1 if the document’s parent is 0, meaning it’s a root-level document.
Or, we could go with the standard DropMenu and the "ultimate parent" snippet, and make another snippet that will replace your side menu’s opening container <div>, if the document’s parent is 0 it will generate a <div class="hide">, and you can simply hide it in the CSS, while it the document’s parent is not 0 it will generate a <div id=#sideMenu>.
Option 2 is the simplest. Option 3 is good for compatibility; it will work with any menu snippet.