Cygwin Icon Broken In Taskbar
I encountered a similar problem on a newly installed 32-bit Windows-7 Ent machine. I had the Cygwin Terminal pinned to the task bar and got the broken icon whenever a terminal was invoked. Subsequent terminals stacked under the broken icon.
I right-clicked the pinned icon, right-clicked "Cygwin Terminal", clicked Properties and changed the target from "C:\cygwin\bin\mintty.exe -i /Cygwin-Terminal.ico -" to "C:\cygwin\bin\mintty.exe -"
Now there is no broken icon and all terminals invoked stack under the pinned icon.
HTH Tom Crane