Help Using Original R4 With NTRBOOT HAX

Picture from your card pls. Btw is here a list with all compatible flashcards.

 

You have been linked to a list of compatible flashcarts, if yours is not on that list then it is not compatible.

 

As far as I know the original R4 came out before the DSi. With the DSi (and later the 2|3DS) Nintendo started blocking DS flashcarts by putting all DS games that existed to this point on a whitelist – later DS games are digitally signed.
If a cartridge neither is on the whitelist nor contains a valid signature the DSi (2|3DS) refuses to load it.

Later flashcarts contain at least parts of ROMs from the whitelist to get around this check. [background information→ https://hackmii.com/2010/02/lawsuit-coming-in-3-2-1/ ]
For a while Nintendo played a cat and mouse game with flashcart manufacturers. Each update blocked known flashcarts with better checks. Firmware updates changed the game the flashcart tries to mimic. [For example see: https://wiki.gbatemp.net/wiki/Updating_the_AK2i_Bootloader]

But as the DS-Lite and DS-Phat did not have such a check… I don’t think the original R4 can get firmware updates at all (the firmware is not the kernel on the micro-SD). Without the possibility to upgrade (rewrite) the firmware, there is no way to replace the firmware with ntrboothax.