You know in reading through all of this again, couple things I missed...you say these removed items ended up in your Recycle Bin...Why? Normally if my antivirus program removes something it is sent to the Quarantine OR just plain deleted, not to the Recycle Bin but deleted.
The other thing you say, these were supposedly viruses or trojans but what showed in the Recycle Bin were two Windows Installer Packages and the file sizes were just about right for the Windows Installer 3.1
I am wondering, were these uninstalled by mistake?
Look in Add/Remove and see if it is listed there, should be there but I also don't see it on your Uninstall list either.
You do need this to install many programs, maybe that is why you can't get the Quickbooks to install
Go
HERE and download and see if that helps. Meanwhile I will take a look at your log.