This is a very common problem on early Z4s.. up to 2006 I believe. The electric motor is housed under the passenger side upper rear wheel well.

The pump is wrapped in foam to make it a quiet up and down. water finds it's way into the wheel well when the drain holes get blocked..which they do very often... The hydraulic pump sits in the water..water soaks into the noise resistant foam..pump fails.

Almost every driver of a Z4 I know has this issue. Replacing the pump is costly and time consuming..4-6 hours..at one point in the process 2 people are needed to remove the roof, and put it back..it takes some expert maneuvering, and if not careful the body paint.along the back seats as well as the rollover bars will be marred. The pump retails from 450 usd to 550usd. Labor can run about the same or more in a shop...Many screws, clips, door moldings must be removed working in the confined space of the trunk... Aware of of this problem, I went to look at the Z-4 I ultimately purchased ..I loved the car..everything I was looking for..asked the salesguy to put down the top for me .. he had a sheepish look, tried it..nothing..just a light buzzing sound. I told them I would take the car if they fixed the top..and I wanted to be there to watch them..

they agreed..also made them pay for a second BMW key...from BMW $235.00... heard a clicking in the starter..made them replace that too.

Back to the top...some guys when they replace the hydraulic pump, remove the foam wrapper, cover contacts with silicone. or place the pump elsewhere..behind seat in the cockpit. There is also a cheaper fix...the hydrualic pump can be bypassed by pulling out a red lever to the left in the trunk..then you can very easily lower and pull up your top by hand...one person job.

But the auto hydraulic pump does such a nice job...when it is working.