My initial attempts to get the latest version of Tiny Core Linux to run on the DX-3000 resulted in failure.
Along the way I found adding the command line parameter of acpi="off" did get it to stagger along
and get as far as a shell prompt, but no matter what other parameters I added, the keyboard was always dead at this point.
After a while I realised that, as the BIOS in this machine dated back to 2015, the problem probably lay in various enhancements/updates that had been added to a standard BIOS over the last eight years some of which the kernel now assumed to be present. The solution was to go back in time. Sure enough Tiny Core 7 from 2016 ran without any problems.
A quick test showed that Tiny Core 7, 8, 9, 10, 11 and 12 all ran. Versions 13 and 14 didn't. Version 12 was announced in February 2021 and used kernel version 5.10.3. Version 13 was announced on 31st January 2022 and used kernel version 5.15.10.
So to run your particular flavour of Linux you may have to look for an earlier version of it. The 5.10.3 (working) and 5.15.10 (not working) kernel version numbers noted above can help you in your selection.