If it's FTP and FTP only (you made it to serverfault, so I guess web browsing works) then my first guess is that your router/firewall has ended up configured to block FTP. Dead hardware would almost certainly affect everything equally (especially if these ftp sites are unrelated, so they wouldn't be connected through a VPN or some other special network connection). If it's a fancier one (say, a Cisco PIX instead of a $40 linksys) my first guess is that it was originally configured to block FTP, then later someone came and configured FTP access but forgot to commit the change to flash. Now the power finally blinked, and the unsaved firewall changes were lost.
The problems with this theory are that firewalls are typically configured to drop connections rather than return a connection refused packet, and that most firewalls would allow outgoing FTP by default (as long as you were using passive mode... which wouldn't be an issue until you actually try to download something from the FTP server.