Thanks for your advice. The car does absolutly not move when connected and on with the hexfly battery. So yeah, I followed your advice and mailed redcat. Lets see what they say.
In fact I tried another LI-ION with 700MAh from Carson, with this battery the car moves for like 30 secs and then off..only steering possible. Could that be the ESC, as Redjet mentioned?
Hopefully Redcat is willing to fix it.
Ill keep you posted!