Use a multimeter on continuity mode, one probe on the first wire you soldered to the board and the other probe on a ground point and see if the meter beeps. If not do that again for the other wire. Also maybe look on the pcb and see if you can work out where the copper tracks go.
Maybe you should have a look on google to see how switches can be used in circuits. You will probably find that one end of the switch is common to the rest of the switches.
Basically you should only need to solder one wire to the switch position for the Arduino not two.