Why won't my Vista machine accept 3.6.10?
I have no problem downloading the browser, but when I try to run the download I get the message that (a) the file does not have a valid digital signature that verifes its publisher, and (b) if you try to run it anyway, it says the file is corrupt.
Alla svar (1)
It is possible that your anti-virus software is corrupting the downloaded files or otherwise interfering with downloading files by Firefox.
You can try to disable the real-time (live) scanning of files in your anti-virus software temporarily to see if that makes downloading work.
See http://kb.mozillazine.org/Unable_to_save_or_download_files