|It is possible with a computer but I wouldn't expect to be able to do it with a Windows box.|
What you're talking about is fairly complex. You have to have two external interfaces. The active one has to be monitored at all times. Should the connection fail, it has to change over to the other connection automatically.
I know it can be done with UNIX. We use dual teamed OpenBSD servers for our firewalls/routers that provide just this type of fail over. They utilize VRRP techonology so they both operate on one gateway IP address.
In order to do this, you'd need to be very familiar with UNIX and VRRP. If you're not that fluent in UNIX, then the simple solution would be a dual WAN router that does this for you. Which is why I suggested that at the outset.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.