Kalkhoff Agattu (e-bike) Panasonic 24v engine dead - worth repairing?
First up - I know nothing about your specific bike model.  However 3 years is a pretty good run for batteries especially if used for hill climbing, and it could be they're just past it and need replacing.   

600 euros sounds a lot, but its one of the consumables.  Do you know how far you're ridden?  10,000 km would be 0.06 euros per km, which is a lot cheaper than a car.

Its highly unlikely the battery shorted the motor and the motor shorted the battery killing both.

If you're handy, try and find two working 12V batteries (car ones would do) and hook them up in series to the leads, with your powered wheel off the ground.  Do mind the polarity and watch for shorting.  The bike should run like normal on 24V.  For this test, battery type doesn't matter but current will need to be at least 10 amps so small batteries are unsuitable. If this works, the motor is fine.  You might be able to use a mains PSU adapter, provided it supplies 24V DC at 10-15 Amps.

If this doesn't work, the motor or controller may be damaged and you need some more skilled local help.  Google about for an ebike retailer or specialist in your region.

Best to google about for a replacement battery pack or find a battery specialist who can repack your existing battery.

A bike is not a cellphone to be replaced every couple of years, with normal maintenance it should last for decades.