Need to Re-Install Lightroom 6 on my Windows 10 PC

I have purchased Lightroom 6, I was having problems starting it up.  I trying a number of things.  Finally it said I had an error 16 to uninstall lightroom and re-install.  I bought Lightroom 6 online, downloaded and installed it online.  I do not have the original disks.  I have uninstalled lightroom I now need to install it again.  I have talked with Customer care and they cannot help me.  I do have the original serial number to my product.  I need help!