That circuit is incorrect whether the switches are there or not. The anode of the led has to be connected to a power source (Battery in your case). Right now, you have it connected on the ground side of the temp sensor. If you were to take the single wire from all those led's and move it to the TOP side of the temp sensor, you would have a circuit.
You can also think of those switches as the I/O pins, but you would have to add another connection point, which would be ground, and that would be connected to the negative side of the battery. Then via programming, the "switch" could be 5V, Ground, or Floating (not open like you think) If the I/O were set to HI (5V), the led would light up. If set to LOW (Gnd), it would be off. The "floating" part of that switch comes in on inputs. Not going to get into that here, but just remember floating pins.
As for the temp sensor, you have VCC and VSS, but no data line hooked up, so it is working, but you won't be able to see it.