It could be that a firewall (your, your router's, your ISP's...) is blocking all IRC connections. (The server shown is currently online.)
Try connecting using the alternate (non-standard) ports – 6665, 6666, 8000, 8001, or 8002. The Hexchat syntax is irc.freenode.net/6665 in the server configuration window, or /server irc.freenode.net 6665 in command line.
Even better, try a SSL-encrypted connection – the standard port is 6697, and freenode also accepts connections on 7000 & 7070. Syntax is the same but with +port; e.g. irc.freenode.net/+6697 (as in the topmost entry of your current server list) or /server irc.freenode.net +6697.