What happened to my electrical circuitry in my house? It seems like a fuse has blown but it hasn't?

So two plugs, two lights and the doorbell - which would appear to be on the same fuse - do not work. They randomly stopped and I don't know why. There are no blown fuses when I check the circuit box? What is going on? Do I need to hire an electrician or can I fix it myself? How much do would this cost to fix?