Why does my Pi-DOS boot get stuck at the DOS prompt with no keyboard input?

This smells like the classic bootloader vs DOS USB handoff problem. The firmware on the Pi handles the keyboard fine during boot because it drives USB itself, but once DOS loads it has to talk to the USB chip through its own drivers, and those are a lot pickier.

First thing I would try is moving the keyboard to one of the black USB 2.0 ports, not the blue ones. On the Pi 4 the two port types go through different hardware, and I found on my setup that the DOS USB driver only wanted to play with the 2.0 side. Cheap membrane keyboards generally work best here too, since they speak the older simple HID style the driver expects, so your membrane one is the better test candidate. Second thing to poke at is the config. If you pop the SD card into another computer you should be able to see the DOS partition and open the startup files in a plain text editor. There should be a line that loads the USB or HID driver at boot. Check it is not commented out or missing, and check the file name matches exactly what is on the card, capitals and all. DOS is unforgiving about that. Also worth doing: pull the config.txt off the card and have a look, since a setting in there can affect how USB is handed over to the OS. The repo usually has an issues page or discussion tab, and a search for 'keyboard not working' on your exact release will often turn up someone who hit the same wall, sometimes with a one line fix. One more long shot, but try the mouse on its own in a different port after the keyboard test. If neither HID device works in any port but both work in the bootloader, it points to the driver never loading rather than a compatibility issue with specific keyboards, which would make the config.sys check the real culprit.

If all that fails, rebuilding from source is actually less scary than it sounds, but the prebuilt image plus a config fix is usually enought.

Had the same dead-HID situation on mine and it turned out to be the power draw, of all things. The mechanical board was pulling enough current that the driver gave up partway through enumerating it, even though the bootloader had lit it up happily moments before. Powered the keyboard through a small hub and it started typing at the prompt immediately. Might explain why your membrane one also failed though, so prolly not your whole story, but a hub costs nothing to test. Out of curiosity, does the caps lock light toggle once DOS is up, or is it fully frozen?

Following this because I had a similar thing happen with a different DOS image on my old Pi 3. Never got the keyboard going at the prompt either, gave up and just used a PS/2 adapter board I had lying around, wich worked straight away. No idea if that's even an option on the Pi 4 though, so don't take my word for it. Does anyone know if Pi-DOS supports serial or PS/2 input at all? Would be handy to know before I dig out another SD card.

Not convinced the USB 2.0 port thing matters here. Both keyboards dying along with the mouse points away from a picky driver picking on one device, that's a driver that never started at all. When mine went like that on a similar image it was the HID driver line sitting after a memory issue in the startup file, so nothing ever loaded. Swap the load order around before chasing ports.

Been down this road with an old 486 emulator on a Pi Zero years back. Turned out my keyboard needed the driver loaded with a delay after the USB stack came up, something about it not being ready in time. Check if there's a timeout or wait setting near the driver line in the startup files, a couple seconds of patience fixed mine. Also, before anything else, try a keyboard you know has no extra bells and whistles, no built in hub or media keys. Those always caused grief. And burn an older release to a second card if you have one handy, sometimes the newest build breaks what used to work fine.

Update: sorted. Went with the powered hub idea from the second reply, figured the mechanical board was starving the USB side once DOS took over. Stuck the keyboard and mouse on a small hub with its own plug and both came alive at the prompt right away. No rebuild needed, which was a relief. Back to playing flight sims from 1994.