It sounds like you're using the old simulator. It's not recommended to use the old simulator because a core plugin used to run the software, web unity player, no longer works in most browsers.
Just scroll to the bottom of the badge instructions and press the Skip Simulator button. This will unlock the badge. Then run the badge mod in Minecraft.
There are currently two 'Skills and Drills' sections in the main badge index. Be sure to select the Skills and Drills: Testing in Vox-L icon at the top of the page .Any badges outside of the Skills and Drills section (Sidekick, Magic Wands, etc) will be eventually moved into the vox-L simulator, during a unscheduled future website update.
If you've made your own mod in the mod.learntomod.com/programs/ area, there should be an option on the drop down menu that lets you test in vox-l. However, alot of the advanced level blocks (any blocks used outside of the skills and drills section) are too advanced to render in that simulator, so I would recommend testing in minecraft
I recommend completing the vox-l skills and drills badges first -- there are about 100+ badges in this section.
Here is how to get the version of minecraft that works with learntomod: Where can I download Minecraft? You can go back to the skills and drills < getting started < run your first mod badge if you can't remember how to connect to our minecraft server.