I have an old IBM Thinkpad 600 which exhibits a green and yellow screen. The way I solved this was to use frame buffer mode as described in the FAQ:-
How to use framebuffer X server?
In order to use framebuffer (Xfbdev) you will need to have a persistent store, e.g., a PPR.
Boot Tiny Core as follows, using an appropriate vga code from the f2 boot help screen and an appropriate disk partition.
boot: tinycore tce=hda1 text vga=788
At the system prompt:
$ tce-load Xfbdev.tce wget install # This is for TC 2.2 and below
$ tce-load -w -i Xfbdev.tcz # This is for TC 2.3 and above
$ xsetup.sh
$ startx
From the X desktop, shutdown with backup. Your Xfbdev X settings will be saved and used on the next boot.
Do not use the text boot code and your framebuffer X server should start successfully.