I think my problem applies to this thread. 
(I'm unclear how to reply to an entry in the mailing list archive)


all cygwin commands stopped working for me, too.
(i have been using cygwin for many years, it has been running on my windows 10 system for as long as windows 10 has been available)
so, i recovered a version of the bin folder from a few days ago, and all is working. (note, i only had to recover the bin folder, i did not have to recover the lib, etc, or var folders)

not sure if i ran cygcheck correctly - i ran it from a cmd window in a non-cygwin folder (this is newcheck.out)
so i ran  it again (badcheck.out) while working dir is \bin.bad (my 'bad' version of \bin folder)
NOTE: i changed the user name changed to XXXX)

Before backing up the bin folder, the situation was:
When i run cmd window and try anything in cygwin bin folder i get (bash.exe is just an example) (except for cygcheck :-)
C:\newbin>bash.exe -i
      0 [main] bash (1588) C:\newbin\bash.exe: *** fatal error - add_item ("\??\C:", "/", ...) failed, errno 22

This also happens with bat scripts i have been using for many years to start xwindows or just a terminal window.

It appears, i think, to be a problem with setup (or maybe an interaction with some recent windows 10 update?), 
since when i run setup-x86_64.exe, i get the following in /var/log/setup.log:

2019/12/21 13:48:56 Starting cygwin install, version 2.897
2019/12/21 13:48:56 User has backup/restore rights
2019/12/21 13:48:56 Current Directory: K:\installation_disks\cygwin64
2019/12/21 13:48:56 Could not open service McShield for query, start and stop. McAfee may not be installed, or we don't have access.
2019/12/21 13:49:01 source: network install
2019/12/21 13:49:02 root: C:\ system
2019/12/21 13:49:03 Selected local directory: K:\installation_disks\cygwin64
2019/12/21 13:49:04 net: Direct
2019/12/21 13:49:06 site: http://mirror.clarkson.edu/cygwin/
2019/12/21 13:49:06 HTTP status 404 fetching http://mirror.clarkson.edu/cygwin/x86_64/setup.zst.sig
2019/12/21 13:49:06 HTTP status 404 fetching http://mirror.clarkson.edu/cygwin/x86_64/setup.zst
2019/12/21 13:49:08 solving: 0 tasks, update: yes, use test packages: no
2019/12/21 13:49:11 solving: 0 tasks, update: no, use test packages: no
2019/12/21 13:49:11 Augmented Transaction List: is empty
2019/12/21 13:49:13 Changing gid back to original
2019/12/21 13:49:13 running: C:\\bin\dash.exe "/etc/postinstall/0p_000_autorebase.dash"
2019/12/21 13:49:15 abnormal exit: exit code=-1073741819
2019/12/21 13:49:15 running: C:\\bin\dash.exe "/etc/postinstall/0p_texlive_prep.dash"
2019/12/21 13:49:18 abnormal exit: exit code=-1073741819
2019/12/21 13:49:18 running: C:\\bin\dash.exe "/etc/postinstall/0p_update-info-dir.dash"
2019/12/21 13:49:19 abnormal exit: exit code=-1073741819
2019/12/21 13:49:22 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/bash.sh"
2019/12/21 13:49:23 abnormal exit: exit code=256
2019/12/21 13:49:23 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/cygwin-doc.sh"
2019/12/21 13:49:26 abnormal exit: exit code=256
2019/12/21 13:49:26 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/lyx.sh"
2019/12/21 13:49:28 abnormal exit: exit code=256
2019/12/21 13:49:28 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/TeXmacs.sh"
2019/12/21 13:49:29 abnormal exit: exit code=256
2019/12/21 13:49:29 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_adwaita-icon-theme.sh"
2019/12/21 13:49:31 abnormal exit: exit code=256
2019/12/21 13:49:31 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_desktop-file-utils.sh"
2019/12/21 13:49:33 abnormal exit: exit code=256
2019/12/21 13:49:33 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_fontconfig_cache_1.sh"
2019/12/21 13:49:35 abnormal exit: exit code=256
2019/12/21 13:49:35 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_glib2.0.sh"
2019/12/21 13:49:38 abnormal exit: exit code=256
2019/12/21 13:49:38 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_hicolor-icon-theme.sh"
2019/12/21 13:49:40 abnormal exit: exit code=256
2019/12/21 13:49:40 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_man-db.sh"
2019/12/21 13:49:42 abnormal exit: exit code=256
2019/12/21 13:49:42 running: C:\\bin\dash.exe "/etc/postinstall/zp_octave_finish.dash"
2019/12/21 13:49:44 abnormal exit: exit code=-1073741819
2019/12/21 13:49:44 running: C:\\bin\bash.exe --norc --noprofile "/etc/postinstall/zp_shared-mime-info.sh"
2019/12/21 13:49:47 abnormal exit: exit code=256
2019/12/21 13:49:47 running: C:\\bin\dash.exe "/etc/postinstall/zp_texlive_finish.dash"
2019/12/21 13:49:49 abnormal exit: exit code=-1073741819
2019/12/21 13:49:50 Changing gid to Administrators
2019/12/21 13:49:56 note: Nothing needed to be installed
2019/12/21 13:49:56 Ending cygwin install