Fully updated cygwin64 on Win10 Pro x64; cygcheck.out attached.

If I attempt this in a regular mintty session, it hangs forever (until
killed with ^C). If I run it in a priviliged session (Run As
Administrator) it gives the below timeout message after about 90
seconds.  And yes, I did as suggested: moving the mouse, running
chkdisk in a CMD box, etc.

===================================
$ gpg --gen-key
Note: Use "gpg2 --full-generate-key" for a full featured key generation 
dialog.

GnuPG needs to construct a user ID to identify your key.

Real name: Jim Garrison
Email address: [redacted]
You selected this USER-ID:
     "Jim Garrison [redacted]"

Change (N)ame, (E)mail, or (O)kay/(Q)uit? O
We need to generate a lot of random bytes. It is a good idea to perform
some other action (type on the keyboard, move the mouse, utilize the
disks) during the prime generation; this gives the random number
generator a better chance to gain enough entropy.

gpg: agent_genkey failed: Timeout
Key generation failed: Timeout
====================================

-- 
Jim Garrison