New to you Z4, were you checking out how things work? Go to your trunk (boot if you're in the UK) and check if the trunk shelve is in the up position. You'll see a knob under the shelve on either end, turn these and you'll see the shelve move up/down a little. Turn the knob's so the shelve is in the lowest position. After doing so try your top.
These knob moves the shelve up/down to allegedly provide more trunk space storage.
However, if you try and lower the top when the shelve is in the up position, to prevent damages, when the top is lowered, the system turns off.
You push top down and nothing starts and there are no lights. This is what you reported is happening to you.
Hope it's simply the shelve because that an easy fix by turning the knob. Good luck