Audio Technica T27 Transmitter: supposedly has the option of 20 different frequencies - does anyone know how to change those?

The unit is a wireless receiver - used with the matched frequency Audio-Technica microphone(s) and musical instrument transmitter packs.

That's called, "interference". Somebody else is broadcasting on the same frequency, perhaps a local fire station or other radio transmitter.

Here's the owner's manual for that series. You'll find the battery replacement instructions on page 6: http://eu.audio-technica.com/en/resources/2000a%20Series%20Owners%20Manual.pdf

http://www.propertyroom.com/l/audiotechnica-transmitter-9-pieces/9371087#

they have units on auction

This could be due to interference from other devices.
You could try changing to a different frequency (there are 20 to choose from).
Also move the receiver away from any strong electro magnetic fields (hearing loop amplifiers, CD/DVD players, TVs) or large pieces of metal and in clear line of sight of the transmitter pack.
Set up the aerials so that they are at a similar angle as the aerial on the transmitter.
Only use xlr balanced cables with good quality screening to connect the receiver to the mixer / amplifier. Keep signal cables well away form mains electricity cables as far as possible.
Wherever possible use balanced xlr cables on all other equipment.

Normally the mics and receivers are sold as a unit but replacement mics can be bought separately.
However the ATW-R11 has been discontinued so may now be hard to find.

This model has 20 available frequencies so you should be able to change frequencies okay.
NOTE - you will require a license for these frequencies

The most common problem with earphones are the wires. Usually near the end. You can carefully open the headset to expose the wire connection, and check for continuity.

No, the ATW-R200 series are fixed-frequency units.
Short of soldering new crystals in, you're stuck with the frequency you've got.

the unit I'm using is old and is on a 200mhz frequency and it uses Vhf, so I have to buy a new unit.....nothing can be done to fix the problem....

If you're handy, you could rig up a wireless solution to this. The problem is that you have two screens, each presumably playing a different movie. If you purchased an off-the-shelf wireless transmitter accessory, you could connect it to one of the screens. But then if you purchased a second wireless transmitter accessory, and connected it to another screen, you would need to make sure both wireless transmitters were operating on different frequencies, so that each person could wear a different pair of headphones and listen to their own movie. Hopefully this makes sense. You could use either an FM Modulator to do this, or an Infrared Audio (IR) transmitter... Remember, these units aren't like factory installed headrest systems; they don't have the wireless audio transmitter already built-in, so you can't just buy wireless headphones and listen to them.