So you wanna remotely access a Linux box? From a Windows machine? The Nomachine NX Client looks like a reasonable option.
To install on a 64-bit (Ubuntu-based) Linux, first download the NX Free Edition for Linux. You should end up with something like the following deb packages:
nxclient_3.5.0-7_amd64.deb nxnode_3.5.0-9_amd64.deb nxserver_3.5.0-11_amd64.deb
sudo chmod 755 /usr/lib/cups/backend/ipp sudo dpkg -i nxclient_3.5.0-7_amd64.deb sudo dpkg -i nxnode_3.5.0-9_amd64.deb sudo dpkg -i nxserver_3.5.0-11_amd64.deb
If all goes well, that should conclude the Linux side installation.
All that remains is to download and install the NX Client for Windows on the Windows machine, and a world of stultifyingly laggy screen refreshes awaits.