There seems to be an endless list of reasons as to why the Forest won't connect. Like Feint said, it can be temperatmental xD Here are some things you can try:

Computer-based:

• Right click the program and select 'Run as administrator'
  
• Double check that your firewall is not blocking the game
  
• Re-start your router
  
• Don't run any programs alongside TEF when you run it (Usually you can open more programs without much issue once TEF is fully connected, though you may lag a little more depending on what you're running)
  
• Run only a browser alongside TEF (It's weird, sometimes this seems to help me. Sometimes it makes it worse.)

Game-based:

• Start the game. Do not touch it; walk away for about five minutes and see if it does anything.
  
• Start the game. Adjust your camera angle a little, make the deer get up, and walk around. As soon as your deer logs in (you see your pictogram), get up again and start walking. Open your orange action bar and click on several of the icons for about 1 minute straight, moo at least once, then run/hop around some. After that, don't touch the game for another minute or two. This one is currently the most effective for me. I don't know why it works, but it does. It'll probably be a different method in a month, lol.
  
• Moo. A lot.
  
• Have your deer pray at the Twin God statues
  
• Jump in and out of the pond
  
• Just run around like crazy
  
• Open your menu and go to 'Network.' Choose 'Disconnect' and wait for the game to re-connect. You may need to click 'Connect' a few times to encourage it, if it gets stuck. Try some or all of the above again.
  
• Open your menu and select 'Quit.' Wait for the game to exit completely, wait about 5 seconds, then open the game again. Try some or all of the above again.
  
• Wait until there are fewer than 40 users online (the server was built to handle 50 at max, so you will probably have trouble connecting during high-traffic hours)
  
• Wait until the weather is back to normal (it's currently night in the Forest, which means more people are logging in and the game has to load the environment changes in addition to everything else; it can make connecting more difficult)
  
• Combine the above in different ways until something works and you find your own method.

Like I said, the game is temperamental, but there seem to be a few consistent tricks to getting it to connect. Once you find a method that works, remember what you did and stick with it. If it continues to work, keep using it until it doesn't. When I find a method, it usually lasts 2-5 months before I have to find a new one because something changes with my connection or the server or whatever it is that makes the game quirky. It can be annoying, but once you get a pattern down it's usually not too bad. :3 Good luck!

Edit: Yes, the box on the left should be green when you are fully connected, and you should not have any 'clumped' pictograms at the bottom of your screen.
Red: You are not connected to the server at all
Orange: You are partially connected. Either your game is not communicating properly with the server, but you are connected and visible to other players (but will not show up on the map), you are not logged in, or you are connected but the other players have not loaded (ie your pictograms have not spread)
Green: You are (in theory) completely connected and logged in