Drag function in Blocks is Gone
It's definitely js related, most likely a conflict/error from something in the theme or a contributed module. If you switch to a core theme, are the blocks draggable? If not, it's probably a module (or a script coming from somewhere else, like a block).

If you need to change block position ASAP, you can temporarily disable your browser's javascript, which should then cause the weight positioning drop-downs to appear, which you can use to adjust the order.