Do you have any previous versions of LR installed on the system??? If so, uninstall them first before attempting the new LR4 install.....and, just to try something different, try installing while NOT logged in as administrator. I've installed LR recently, uninstalled LR2 before installing the new one and I was not logged in as admin, all went smoothly, no probs.
I think it's going to to be a call to the Adobe tech support on Monday, as i have been trying a nimber of thing, checked capability, load as 32 bit instead of 64bit but all without a results.
Try switching off the Internet and closing down or disabling temporarily the third party antivirus program (if you have it installed). Some of them are overprotective. Also, put downloaded file straight onto desktop then start it. Not every folder allows smooth extraction (esp. USB drives).
Problem solved.
Put the advice here in case someone lse has the same issue in the future. Assuming you have the serial number from the purchase.
Delete the download in full off the laptop. Download the try version and then register with the serial number from the original purchase. When I did this I had an issue getting the download to start ,so swapped from IE to google chrome browser and it worked fine.