PS: Mozilla will be eating cake as well as Internet Explorer's marketshare ;)
There is a program called Ping Tunnel to send TCP traffic over ICMP. From the project home page:
Ptunnel is an application that allows you to reliably tunnel TCP connections to a remote host using ICMP echo request and reply packets, commonly known as ping requests and replies. At first glance, this might seem like a rather useless thing to do, but it can actually come in handy in some cases. The following example illustrates the main motivation in creating ptunnel:
Setting: You're on the go, and stumble across an open wireless network. The network gives you an IP address, but won't let you send TCP or UDP packets out to the rest of the internet, for instance to check your mail. What to do? By chance, you discover that the network will allow you to ping any computer on the rest of the internet. With ptunnel, you can utilize this feature to check your mail, or do other things that require TCP.
Absolutely fantastic -- it Just Works. Download ping tunnel here.