and thank you for that.
First of all, I am guessing that the message about "LibO_3.5.2_Win_x86_install_multi.msi is not commonly downloaded and could harm your computer" is either from your anti-virus or it could in fact be from your browser itself. You mention IE9.
Yes, I have just tested the "Main installer" download from the LibreOffice web site in my own IE9, (I normally use Firefox as my browser), and got the same pop up at the bottom.
"Do you want to Run or Save LibO_3.5.2_Win_x86_install_multi.msi (208 MB) from mirrors.coreix.com?"
Then it says, "This type of file could harm your computer" and gives the options "Run / Save / Cancel"
When I click Save, (I always save, and never Run), the pop up changes to show that the file is downloading and offers to "View downloads".
All of that is normal.
But what happens next, (at step 10), doesn't seem normal. The process is the same and I confirm that the installation did take a little while on my Win 7 x64 bit system, the same as it did on yours.
I can see where others have had this problem as well at http://en.libreofficeforum.org/node/2202
By any chance, have you used OpenOffice in the past, or still using it? If so check your Task Manager to see if any elements of OpenOffice are still running and if so end them. If you still have OpenOffice, it might be an idea to uninstall that, reboot, (restart) the computer, then try installing LibreOffice again.
If that fails, see if the other suggestion made in that discussion helps.