First, please make shure that your minecraft is a premium account. Premium is when you have bought minecraft from minecraft.net. Also make shure your password is correct. If your username or password is wrong, then it will say "Login failed". So it is probaly not that due to the fact that is says "Cant connect ot minecraft.net". One way you can fix this is by going to minecraft.net and log out there and logback in. Sometimes you just need to wait a day or so to get back on due you your connection and where you live. Have you ever played online? If it is everytime you log in, you may want to go back and change your password or contact mojang support.
Hope your minecraft gets back up and running.
~DiamondOcelot