https://support.dynabook.com/support/staticContentDetail?contentId=4012710&isFromTOCLink=false
Ubuntu 16.04 LTS works!! lol. I must have tried 15 different distros.
Probably because the older 4.4 kernel has drivers for the old graphics card and support was dropped on newer kernels. That happened on my old netbook, no any drivers on newer kernel versions. 13.04 was the last one supporting it. So stuck with windows 7 for ever lol
Are you sure it’s the kernel version and not the Mesa version? If Mesa, you could continue using an up-to-date distro with just an old Mesa package instead.
Not sure at all… Because i dont know what Mesa is 
EDIT: Ubuntu 18.04 LTS also works.
20.04 also works.