How to get Apple TV 3rd Gen to connect to new Wi-Fi settings with no remote and a TV too far away for ethernet cable connection

If you only want to host VNC on your Lion server I'd suggest opening the specific port for that service (TCP 5900) on your modem/router and forward it to your Lion server, as opposed to putting it on a DMZ which fully exposes the machine to the internet.

To be able to get to your server using a human readable address like - server.mydomain.com, you need to own a domain (mydomain.com) and then link your actual internet IP address (that your internet provider gives you) to that domain (e.g. server.mydomain.com). It's pretty much as simple as that if your internet IP address doesn't change (is static). If your IP address regularly changes, this kind of approach isn't really possible...

The easiest way to get a DNS (human readable) address is to use a service like DynDNS or No-IP. These constantly check what your IP address is and keep internet DNS records up to date with your current IP address. It requires that your modem/router is compatible with such a service, or that you run a piece of software on a machine (your Lion server maybe) that's inside your network.

So;

1) Forward port 5900 TCP to your Lion server (Port forwarding settings in your modem/router)

2) Set up DNS so that you don't have to remember your IP and so that if your IP changes, you can still connect back to it.

3) Enable screen sharing on the Lion server. Tell it which users you want to be able to connect. Set a password.

I'd recommend looking into using your Lion box as a VPN or SSH server so that you can do all these kinds of things over a single encrypted link. VNC isn't the safest of protocols!

I have a new Apple TV and stream from iPhones, iPads and various macs via AirPlay... and love it!

Two places I'd suggest you focus:

• the operating system
  • upgrade to 10.8 (if you don't want to commit to ML, install it on a partition, thumb drive or RAM card and boot from there to AirPlay)
  • while not a principle cause of what you're experiencing, how much RAM does your MacBook have? If you have 4GB or less, upgrading to 8GB is a small dollar investment that provides a great return in speed.
• the wireless router
  • are you experiencing slow or choppy wifi performance anywhere other than AirPlay?
  • does your MacBook Pro intermittently drop its wifi connection even when you have a full signal?
  • what wireless router(s) do you have, and how old are they?
    • just because it says G or N doesn't mean the wifi router is "any good" or supports all the protocols needed for AirPlay
  • how far is the wireless router from your tv and MacBook?
    • within reason, the closer the better

You call yourself a technophobe and moron, and I'm not here to dispute either of them (but I think you can achieve what you're hoping for!). My simple suggestion to resolve your problem: replace your wifi router with an Apple AirPort Extreme (less than $200) or AirPort Express (about $100).

• I have used macs and iOS devices with a number of different brands of wireless routers, to limited success and happiness, usually defendant upon the age of the router. Older wifi gear does not support all the tricks and new technology Apple (and Intel) builds into the newer computers.
• I've had the best success with Apple's AirPort Extreme or Express base stations... for working with both Macs and Windows boxes.
  • the AirPort Extreme let's you hook up a USB hard drive as a centralized TimeMachine backup disk for all your Macs backups
  • both the Extreme and Express let you attach a USB printer for remote printing

Either of the two routers are quick to set up, work with your Internet gateway, and should accomplish what you need. If you have an Apple store nearby, swing by and pick one up. You already have the software on your MacBook to configure it.

Good luck!