Hope this isn't late. Bad tech support. If you're having problems, just come to the forums. What is your minecraft doing? You just said it's not working but do you have any mods? Texture packs?
What Azrath said. If you connect to servers hosted farther away from you, you're destined to get a worse ping. Try connecting to servers in your country or closer to you.
I'd recommend using TechnicLauncher for things like this. It's much easier and faster. All I can see from the report is that some coremods don't have an annotation and that the FML Injection failed.
To possibly fix: Use Technic Launcer. It's a safe place to use your account to play mod packs on widely used by most people who play mod packs, including myself. Here's the link to the LitW mod pack on technic. http://www.technicpack.net/modpack/life-in-the-woods-20.374084
