The controls of electric water heaters are designed so that at no time are both the top and bottom heating elements energized. Nearly all electric water heaters of this capacity in the US & Canada (other places, too) operate on 240 Volts.
When the water in the tank is below the set point of the thermostat (in your case - 120 degrees), the top heating element is expected to be on - (unless there is an issue with the top thermostat or limit switch). The top most control is the "high temperature limit". It is identified by the reset button on it. Make sure this isn't tripped by depressing the button. If it clicks - it was tripped and should start to make hot water at this point. If not tripped, you should check for the presence of 240 Volts between the heating element terminal screws. Do not measure from ground to a terminal screw and believe 120 Volts is "good". To make heat, you need 240 Volts - not 120 Volts measured across the terminals - not to ground. The amount of heat created running at 120 Volts is only 1/4 of what it will do at the correct voltage.
If you don't measure 240 Volts on the top element, check the bottom element in the same manner described for the top element.
If unable to measure 240 volts on any element, either there is a problem with the power source (blown fuse or circuit breaker), high temp limit switch, or thermostat(s).
If 240 Volts is present on either heating element, and water is not warm / hot in 30 minutes or so, a defective heating element is suspect. You can change controls without draining a tank, but replacing elements will require draining the tank first. Do not power the water heater without first filling it.You can read a very detailed "how to" article about checking water heaters here.
I hope this helps - and good luck!