It does seem fairly clear at this point that the eMMC isn't being recognised at all. No-one seems to have thought to check if any swap is active run the command "free" to check what memory (including swap) is available and free, I would expect it to say there is 0 swap available.

It might still be of interest to see if there are any errors regarding the eMMC in dmesg, so how about saving the output to a text file on a SD card, put a SD card in and runthen you can upload the file or copy and paste it from your PC.