seaken64
When you boot the CD of antiX-19 Base you are brought to a menu. There are two choices for you to try instead of the first one on the list. One will say something like Safe Video, the other will say something like FailSafe. Try them both.
You are probably having a video driver issue and that can lead to a blank screen due to how the X system in Linux works. If it chooses the wrong driver for your graphics card you get poor results. The Safe modes will choose a more generic video driver that will most likely work to get you a GUI desktop but may be less attractive than your hardware is capable of. Once we get to a desktop we can start playing with different driver modules to get the laptop to display it’s best video resolution.
When you load Puppy what video driver is it using? That can be a clue as to how to boot antiX or other Debian derivatives such as Q4OS or MX.
I run much older equipment than your R40e. I’m sure we can get antiX running on that equipment. I have antiX on an old ThinkPad 600e and an old Dell Inspiron 7500. My Thinkpad R61i is closer to your equipment and it runs MX.
Seaken64