"Play Offline" But I have a internet connexion

Hi,
First, sorry for my English, im French :/
I have to go to hospital many times, and when i am at the hospital and when i launch the launcher, the big button where usually i see "Play", there is writed "Play Offline" and, then when i click on this button, i cant connect to multiplayer servers. But, i have an internet connexion, i can check my mails, go on Facebook, look Youtube,... What can i do ? Do you have an idea of what that can be ?

I use the launcher Minecraft 1.6.70, but this happened since a lot of months.