Are you sure it says "världen" (the world)? I bet it actually says "värden" (the host)
Anyho,
I noticed that you've been online at "layout test" for quite a while now. Is that a server that you are hosting locally or is it a remote server?
I don't think pingtest.net won't be of much help since I think it only measures ping response times. The stability of your connection is more interesting.
To start off, I'd suggest the following.
Before you start LFS, bring up a command prompt and type:
ping -t google.se
The -t switch will keep the ping loop running continuously, so while it's still running, start LFS and connect to a remote host. Should the connection fail, quit/alt-tab out of LFS and have a look at the output of the ping command (also scroll up a bit and look at the previous messages). Is it displaying response times or error messages?
If everything is looking fine in the ping output, something weird is going on with LFS or the connection to the particular host you were connected to.
If the ping command also fails, something is most likely wrong with the connection to your router or the router's connection to the internet.