I have debugged a little bit. In the unit "OverbyteIcsHttpProt" in class "THttpCli" in method "DoRequestSync", and in the while FState <> httpReady do loop the state (FState) is always "httpDnsLookupDone", but does not change any more.
I looked a little bit deeper into unit "OverbyteIcsWSocket" into procedure TCustomWSocket.Connect where the method "WSocket_Synchronized_Connect" is being called, and this method returns 10035.
I searched again in the internet and found the following site: https://stackoverflow.com/questions/16488603/overbyteics-http-timeout-when-used-in-different-threads
And the S O L U T I O N is very simple: DO NOT CREATE THE ICS OBJECTS AT THREAD CREATION TIME, create and destroy them every time you need them in the thread!
Hope, this helps to save others time in future