I am aware of what HAProxy does, but what if my HAproxy goes down?

Or what if my DNS servers go down? Yes, dns is less the problem. However dns only solves to an IP and an IP is announced via BGP to be routed over some router. What if that router goes down?

Of course if I have complicated application servers that are likely to fail HAProxy can significantly improve uptime. But my application isnt.

In fact my application may very well just be delivering a small static html file via HTTP.

Basically if any user anywhere types in MYDOMAIN.COM, I want the user to get SOMETHING on the screen other than a timeout or DNS resolution error.

How can I do that?

The point of entry is difficult. The so called "initial closure mechanism".