I have stumbled across the same issue the other day when I was trying to install Cygwin on Windows 10.
When researching the problem, I found something about an address mismatch in the setup log (sorry that I don't have the exact wording - I won't reproduce that error ...). That lead me to the idea that it might have something to do with ASLR (a technique to harden the system against malware).
So I turned off ASLR. After doing so, I could install Cygwin without problems.
As said above, this was with Windows 10. But to my best knowledge, Windows 7 also has ASLR, so this could very well be the source of your problems. You can turn it off in Windows via UI if you download EMET, or via registry (see here). So you could try that and see if Cygwin then installs correctly.
Please note that I do not recommend having ASLR turned off; I am considering it as an important malware protection. However, in Windows 10, you can enable ASLR per executable, meaning that you can turn it on system-wide and make exceptions for the Cygwin executables. I am nearly sure that you can achieve the same in Windows 7.
In short, you could
turn off ASLR system-wide and install Cygwin
turn on ASLR again system-wide
if the Cygwin installation did not fail, except the Cygwin executables from ASLR
That last step could mean creating dozens of exceptions, though, but for me, it's worth it.
Before that you have already other issues
– matzeri – 2017-05-12T11:00:41.250dash 7004 fork: child 5240 - died waiting for dll loading, errno 11
. Something is interfering with Cywgin. Usually an antivirus https://cygwin.com/faq/faq.html#faq.using.bloda@matzeri I disabled my antivirus and am still having the problem – ewok – 2017-05-12T15:18:56.633
@ewok I had this problem and had to uninstall my antivirus (avast). Cygwin then installed correctly. I then reinstalled the antivirus (I haven't tried to add any new packages to Cygwin since). – DavidPostill – 2017-05-15T22:26:46.277