This is a just mismatch of the video driver by Slax. It is a frequent error in Linux because of the generic drivers being used. Sometimes it can also be due to the monitor frequencies or a fancy keyboard/mouse. Basically Slax fails to get the X Windows up using its drivers to match the detected hardware.
The standard operation of a Live CD like Slax is to boot up the PC and use the "ram memory" to hold the Linux filing system in transit. The hard disk is never touched unless insisted on by the user, like writing and transferring data in the "mounted" partitions which Slax will mount all of them automatically, include Windows NTFS partitions which are mounted with ntfs-3g suitable for writing on them.
The cure of a mismatch video driver depends on how far Linux has got. If you press ctrl+alt+backspace and get the BASH shell terminal then you can fix it by running
You need to know the video card though where it is a "nv", "radeon", "ati" or "vesa" etc. Most video cards will run satisafctorily with "vesa", which is the common standard Slax uses by default, but occsionally you can hit problems.