It's a big tank of water that is heated up. This one only heats up overnight when electricity is cheaper. It is *not* on-demand.
Make sure the time is adjusted correctly and (if it is working) you will have hot water in the morning.
I assume the booster allows you to manually heat the water when you need. If that is not working then yes, it could.be broken. Your landlord should send someone out ASAP.