Yes, I have also a steady red light (the one in the middle).

Thanks for your help, @Lytmi & @Lukas. I've tried everything you proposed, but got still the same result. Then I opened a guest WLAN on my router and was able to connect the Neo box instantly. So seems it's something with the old WLAN? Maybe not supported characters in the SSID oder passwort? Don't know. But now it works, so everything is fine for me.