Missing cygwin1.dll Simple Fix: Put Cygwin in PATH
If you try running Cygwin from another program (say, the Ponderosa tabbed terminal emulator) and you get a "missing cygwin1.dll" error, you should check that you have put Cygwin into your Windows PATH environment variable. Cygwin does not do this by default.
(Documented in the Cygwin manual "Chapter 2. Setting Up Cygwin", section "Environment Variables" (but missed by me on the first pass).)