Did you try downloading from www.getfirefox.com? Try using another browser (such as Internet Explorer) and instead of clicking "Run" click "Save". Then, after the file is downloaded, double-click it to download.
What security software do you have installed? try to disable it and then download again.
Download and Install MalwareBytes Anti-Malware, run a full Scan. http://www.malwarebytes.org/. This helps check that there are no viruses on your computer causing issues. You can uninstall this program after you clean off any infections.
Or, download from another computer, transfer the file to a thumbdrive, then install it on your PC.
Which security software (firewall, anti-virus) do you have?
It is possible that your anti-virus software is corrupting the downloaded files or otherwise interfering with downloading files.
Try to disable the real-time (live) scanning of files in your anti-virus software temporarily to see if that makes downloading work.
See "Disable virus scanning in Firefox preferences - Windows"