That's very strange. Which browsers and version numbers have you tried? Is it feasible for you to switch to a different laptop or desktop? If possible, try switching to a different type of browser.
We definitely don't recommend using the simulator in the old interface - that hasn't been updated in forever; eventually we're planing to do away with it altogether. If you do use the old interface, we recommend scrolling to the bottom of the badge instructions and pressing the skip simulator button then testing in minecraft.
It would be great if you could take a screenshot of what happens when you try to run a mod in the simulator. Then I could pass it along to our Development team. In addition to that, it might help our Development team investigate if you took a screenshot of any red error messages you find in your browser's console. (on Chrome it's ctrl + shift + i)