Pair remote ipad app with apple tv 2 that has no home sharing enabled and no hardware remote
You can use the iOS "Remote" app to control iTunes on your Mac or PC.  As part of this, you can change the audio output from the computer to any AirPlay device on the network, including the Apple TV.

You cannot, however, directly control the Apple TV's GUI.  Buy a new Apple remote, or a universal remote (love my Harmony Ones!).

If the LAN cable is a big deal, you might be able to solve that plugging the ATV into your Mac or PC (needs a micro-USB cable, though, which isn't too common yet) and then doing a restore.  This should remove the static IP, but it might also require you to walk through some setup menus when you next turn on your ATV.  That would be a problem without the remote.

I'd get a new remote, and then I think you can fix ALL the problems mentioned here.