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cvkemp - as others have said Chrome shouldn't be doing the install - msiexec.exe should do the install. Have a look at the file association for .msi files.
Here are the file sizes and checksums for the 32bit and 64bit msi files I have downloaded from the calibre downloads area.
Code:
32bit 60.8 MB (63,836,160 bytes)
CRC32 25893d5a
MD5 80e2d2e15e130c4c759318f69d5a1c49
SHA-1 95fabe784521e9bd2b33fc7ce27fb8d79d7d0d08
64bit 66.2 MB (69,439,488 bytes)
CRC32 76c0e56f
MD5 3537394c9213ed57c7974855d8208c51
SHA-1 c98c0b69be7ff001433be11cf06b28262fe26d7d
The 32bit 2.17 was downloaded within the past hour from
http://calibre-ebook.com/download_windows using Chrome Version 40.0.2214.91 m (which is vanilla - ie no addons, extensions etc).
I double clicked C:\Downloads\From Chrome\calibre-2.17.0.msi to install it. Windows asked me if I trusted the source of the file - I clicked Yes and then Trusted Installer kicked in to do its job.
I then did scans with malewarebytes and adwcleaner, no malware was reported. I also ran a very aggressive malware removal tool which also found nothing (I wont name it because it can create havoc if used indiscriminately).
If the Windows install was done from a a third party slipstream then that is possibly the source of the problem. The safest way to reinstall Win7 is to download and install the official iso with the SP1 slipstream from MS, and then keep running Windows Update until it runs out of things to do - tedious to be sure, but safest for certain.
3rd party slipstream installs are notorious as vectors for malware.
BR