semi automatic problems

[Kod]

I recently purchased a second hand Yaris semi automatic - there was a problem - the car kept on stopping when driving. I got the clutch changed and whilist the problem of stopping when driving is gone there are exists another problem. Sometimes the car does not start or intially it starts but when I change the gear to E position it goes onto N and then it will not move - on restarting the car just goes dead. The situation remains for around 20 minunes after which it will be OK.
Any suggestions?