First of all, you have 240V water heater because tank has two elements.
You have no hot water, and tank has power to upper element.
Lower element has no power.
Something doesn't sound right.
You're not testing correctly.
Before doing anything, test across top two screws of upper element for 240Volts.
This will eliminate electrical problem as suspect.
Breaker must deliver 120V on both legs to complete the 240V circuit.
Every single-phase household circuit takes 2 wires to complete the circuit.
With 120V you need 1 neutral wire and 1 hot wire to complete circuit.
With 240V you need 2 hot wires, one from each hot busbar, to complete circuit.
Your water heater can appear to have electricity if breaker is delivering power on one leg of the 240V circuit.
To check breaker for sure, move wires to another similar size breaker to see if water heater functions properly.http://waterheatertimer.org/B220C.html
If 240V circuit is good, then next thing is take 30 minutes and do full test of water heater parts.
This will identify exact problem(s) without guessing.
Buy 5$ multimeter from Home Depot. Install battery.
When test calls for continuity, rotate dial to Ohms (upside down horseshoe is ohms).
When test calls for testing voltage, rotate dial to 240-250-277 VAChttp://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html
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