I have recently encountered the same issue that Sigil 0.7 and 0.8 version can't launch on Win7 32bit. After a long time testing, it seems the Sigil has a dependency over OpenSSL. After downloading OpenSSL 1.0.1l version and putting the 2 files libeay32.dll and ssleay32.dll into the same folder as sigil.exe, it works fine. You can also put these 2 files into c:\windows\system32. I hope it helps you too.
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