I have a situation where I want to connect to a Linux machine running VNC (lets call it VNCServer) which is behind two consecutive Linux machines i.e., to ssh into the VNCServer, I have to ssh into Gateway1 from my laptop, then from Gateway1 shell I ssh into the Gateway2 and then from that shell I finally ssh into VNCServer. I cannot change the network design and access flow Laptop-->Gateway1-->Gateway2-->Server. I have no root privileges on Gateway1 and all ports except 22 and 5901 are closed.
Is there a way by which I can launch a VNC viewer on my laptop and access the VNCServer? I understand that it might be done using ssh tunneling features and I have putty on my Windows laptop (sorry, no Linux or Cygwin etc. can be installed on the work laptop). Any help will be greatly appreciated as this would make my life so easier!