I'm sorry about the wait. The development team is a small one and they're currently working on other projects. Making major upgrades to the simulator is a project that takes a lot of time and resources (more than one development team member working together at the same time). I'm not sure when it will happen, but last I heard, eventually the old simulator type badges will be moved into the new vox-l simulator.
It would help if you send post some screenshots of what you see in your minecraft launcher, but here are some general tips. (To take screenshots in minecraft, press f2 or fn + f2 on the keyboard then look the minecraft < screenshots folder on your computer.)
Just to make sure we're on the same page, here is run your first mod badge which contains sceencapped instructions: http://mod.learntomod.com/badge_builders/2824?sequence=9054&position=1
Try getting a new 10-15 minutes ip from here, because I'm guessing your old ip has expired by now, as it's been more than 15 minutes: https://mod.learntomod.com/server_instances/current Press the start server button.
Make sure you're using a 1.9 or 1.9.2 profile: http://forum.learntomod.com/t/use-minecraft-1-9-2-w-new-ltm-servers-heres-how/3054/3 -- press play then multiplayer and direct connect and enter the ip. After being transferred to your private world on our server ...
When you press 9 on your keyboard, the mod chest should appear. Then, press the mod button on a badge page, let's make it an easy badge mod like "write your first mod". The mod should then appear in your mod chest.
If it hasn't, then here are some troubleshooting steps: https://learntomod.freshdesk.com/support/solutions/articles/12000012544--you-don-t-have-scriptcraft-evaluate-permission-