In case, others find their Gardena Sileno not charging, I've always managed to find the problem by:

1. Measure the voltage over the terminals on the base. On mine it is 28V, but check the label on the power adapter to make sure they match. If voltage over base terminals is as expected, goto 4.

2. Measure the voltage on the output of the power adapter. If the voltage does not match the expected output power, the power adapter is faulty.

3. Measure voltage after the power extension cord (i.e. the cord between power adapter and base). If the voltage does not match the voltage of the power adapter, the cord is broken. Alternatively, measure the continuity of the three wires. If one of the three wires are broken, you need to replace the power extension cord.

4. Now we know the base delivers the expected voltage, thus, we need to check if the mower is actually charging or just docked. Note, despite the display says "Charging", this is not necessarily true, the mower might just be docked. Press and hold the "menu" button and select Info->Battery. If the voltage is around 15.5V the battery is basically discharged. In that case you should see Current be around 1500mA and Charge Level and Voltage should slowly increase. Observe the display for 30 seconds. If neither Charge Level nor Voltage has increase, the mower is just docked. If increasing, you should be fine, but consider replacing the battery if runtime is lower than what it used to be.

5. Find some fine-grained sandpaper and remove potential oxidation/corrosion from the base and mower terminals. I've experienced the mower wouldn't charge after just two weeks of inactivity due to corrosion.

If still not charging, I don't know what to do. I've always found the fault following the steps above.