What is free solution available. I need to do two things:
1. Connect at machine in same office. I cannot use RDP as it is KDE Mandriva machine.
2. Connect fro home to that machine without VPN i.e over internet


putty fails to connect. I use local IP
And one more thing, SSH is not graphical right? Is there a graphical solution?

If Putty isn't connecting then I'd assume that either Mandriva isn't configured as an SSH server or that the firewall is blocking you. Make sure that you have the ssh daemon running and that port 22 is open (or whatever other port you have configured ssh to run on).

SSH is usually command line, however you can enable X in the config file. Then you can run gui applications over the network. It's the only option that I can think or aside from vpn and rdp which you mentioned aren't options for you.