Cookbook's IPsec VPN with FortiClient does not work - how to find out why

I should setup a dialup VPN from my Windows 10 laptop to my office's FortiGate 30E. As first tries based on the FortiOS Handbook didn't work I followed the FortiOS 6.0 Cookbook recipe "IPsec VPN with FortiClient" (https://docs.fortinet.com/document/fortigate/6.0.0/cookbook/589121/ipsec-vpn-with-forticlient) and implemented it with adjustment of the local lan network addresses (firewall address) only. On my laptop I installed the free FortiClient 6.0.7 and set it up as advised by the Cookbook.

But I had no success, no log entry in VPN Events of my FortiGate and this was the log of my FortiClient:

06.07.2019 18:15:21    Information    VPN    id=96602 msg="SSLVPN service started successfully." vpntype=ssl
06.07.2019 18:17:20    Information    VPN    id=96566 msg="negotiation information, loc_ip=192.168.128.61 loc_port=500 
  rem_ip=(public IP addr of my FortiGate) rem_port=500 out_if=0 vpn_tunnel=NITvie FCT-VPN1 action=negotiate init=local mode=aggressive stage=1 
  dir=outbound status=success Initiator: sent (public IP addr of my FortiGate) aggressive mode me" vpntunnel="NITvie FCT-VPN1" vpntype=ipsec
06.07.2019 18:17:32    Warning    VPN    id=96561 msg="locip=192.168.128.61 locport=500 remip=(public IP addr of my FortiGate) 
  remport=500 outif=0 vpntunnel=NITvie FCT-VPN1 status=negotiate_error No response from the peer, phase1 retransmit reaches maximum count..." 
  vpntunnel="NITvie FCT-VPN1" vpntype=ipsec
06.07.2019 18:18:27    Information    VPN    id=96566 msg="negotiation information, loc_ip=172.20.10.2 loc_port=500 rem_ip=(public IP addr of my FortiGate) 
  rem_port=500 out_if=0 vpn_tunnel=NITvie FCT-VPN1 action=negotiate init=local mode=aggressive stage=1 dir=outbound status=success 
  Initiator: sent (public IP addr of my FortiGate) aggressive mode messa" vpntunnel="NITvie FCT-VPN1" vpntype=ipsec
06.07.2019 18:18:39    Warning    VPN    id=96561 msg="locip=172.20.10.2 locport=500 remip=(public IP addr of my FortiGate) 
  remport=500 outif=0 vpntunnel=NITvie FCT-VPN1 status=negotiate_error No response from the peer, phase1 retransmit reaches maximum count..." 
  vpntunnel="NITvie FCT-VPN1" vpntype=ipsec

- the public IP address of my FortiGate was correct

- it looks like the SSLVPN service of the FortiClient tried to connect to the FortiGate

- but already this action looks like it was not successful

- in a second round an IKE1 negotiation was started, also with no success as the FortiGate did not respond.

(As in previous tries with guidelines from the FortiOS Hanbook I was able to establish a successful IKE1 negotiation the basic setup of the FortiGate looks ok.)

As the log of VPN events is very lean in general I got no hint from the FortiGate what needs to be fixed.

Any hints what I should investigate?

Thanks,

Michael