I WISH TO DISCONNECT ONE TERMINAL OF MY BATTERY FOR AN EXTENDED ABSENSE. DO I NEED TO TAKE OFF ANY PARTS TO FIND THE TERMINALS?

Yes it can be; or it could be that the battery is dead (or bad).
Disconnect the cables, clean the battery terminals, clean the inside of the cable ends. Connect a battery charger, let it charge for at least an hour (don't just use jumper cables from another car). Once charged try it. If you still get nothing, it could be that the battery is shot. In that case, replace it.

Underneath the air cleaner housing. To remove and replace if you can start the car turn steering wheel fully to the right or remove tire. Open hood, disconnect remote battery terminals, remove air intake filter box, remove vented panel inside front of right wheel well. On these cars you will have to disconnect exposed positive cable battery terminal first. BE CAREFUL YOUR WRENCH DOES NOT TOUCH ANY METAL WHILE REMOVING TERMINAL FROM BATTERY POST. Loosen and remove the two bolts on the tie down that secures battery in place. Slide battery until the negative terminal is exposed, disconnect and slide battery out into wheel well. Reverse order to install new battery.

disconnect the battery cables, negative first.
then clean the terminals, and check everything.
If you want, put some grease all over the positive terminal. and it will never corrode.

during the disconnect, the computer will re set to a certain degree, and only on some cars but at least you know its not the battery terminals now. if you want clear the codes then you get a parts man at o'ri, or the zon

Take the bolt out completely.

First off the gas thing might just be coincedence, second sounds like an alternator problem to me. Try this make sure you do not leave any lights or doors open for the battery to drain at night, Make sure your battery terminals are clean and tight, then to test to see of it is the alternator start the engine and with it running disconnect the battery terminals. I can not remember if it is the positive or the negative terminal to disconnect, so carefully start with the positive then the negative terminal and disconnect them from the battery. Be sure to not let the terminals touch any metal while one side is still connected to the battery. If the alternater is bad the car runs only on the charge of the battery, so once the terminals are disconnected from the battery the car will die. If it stays running then the alternator is good. Then I would look at the starter, TO be honest the only way I can truly diagnose the problem is to see for my self. To see if there are any noises, signs of other issues, Or clues that would help rule out the number of possibilietes.
Hope this helps

Here's a diagram that helps

http://www.autozone.com/autozone/catalog/parts/jobDiagram.jsp?engineCyl=5&ymmeId=2006/54/10/78&categoryDisplayName=Batteries&productType=00&parentId=175

pretty much, take off the old terminals, if theyre good, just replace the battery and screw them back together. they might need a cleaning, so get a cleaner for it at an auto parts store, someone working there can give you an idea of what to look for. disconnect the negative first. then positive. take out the battery. there might be a wedge under the battery holding it down so it doesn't move. loosen the bolt to be able to get the battery out. put in the new battery in the same position the old one was, tighten the wedge, then then connect positive terminal, then the negative terminal.

Sarah

1. Ensure you are using the correct spec replacement battery.

2. In many vehicles the radios and sound systems will cease to function if the battery is disconnected and require the radio code (supplied with and unique to the vehicle) to be punched in to activate the unit once power is restored.
I am not sure if the 2000 Mustang has this feature.

Make sure you have turned off all electrical functions on the car and remove the key from the ignition.

3. Batteries are dangerous as they emit explosive gasses which can ignite easily with one spark.
Do not change the battery immediately after running the car. Open the bonnet and allow air to circulate for a while before changing. Wear protective eye wear and clothing when working with the battery and remove metal objects such as rings ,watch bands, bracelets etc. as these could accidentally touch a battery terminal and cause a spark. (Be careful as I have personally seen a car battery explode when gas emissions have ignited with a spark).

4. Disconnect the cable from the negative ( - ) terminal first. Using a spanner, loosen the nut on the cable end and gently remove the cable from the battery terminal. You may need to move it around a little on the terminal before it slides up and free. Disconnect the cable from the positive (+) terminal second by loosening the nut and gently removing the cable. Move the cables out of the way and place a plastic cover wrapping over both cable ends so they do not accidentally contact an exposed battery terminal.

To eliminate risk, wrap some plastic electrical tape around the old battery's terminals before removing it. This ensures no accidental contact with metal parts of the car when moving the battery. The new battery should have a plastic protection cap over each terminal. Do not remove these until the new battery is secured and you are ready to re-connect the cables.

5. The battery clamping system will need to be released to remove the battery.

6. Check the metal cable terminals for corrosion (the presence of white ashy material). They will need to be cleaned up before connection to the new battery to ensure good contact.

7. Install the new battery on the battery platform ensuring it is firmly and properly seated and clamped with the clamping system. Ensure it is properly secured before re-connecting the cables.

8. Connect the positive cables to the positive (+) battery terminal first and then the negative (-) second. (The reverse of removal). Do not overtighten the nuts on the cables when clamping them to the battery terminals.

9. I usually run a very light and thin smear of petroleum jelly over the metal cable ends and top of the battery terminal once everything is clean and connected up. Now replace the protector cover (if fitted to your vehicle)) over the positive cable end and you are done .

10. If your car radio is coded, disconnecting the battery will clear the code on the radio so ensure you have the code available to reset the car radio after the battery is reconnected.

REMOVAL & INSTALLATION 4A-F, 4A-FE and 7A-FE Engines

1. Disconnect the negative battery cable.
2. Remove the air cleaner assembly (with hose).
3. Disconnect all the wiring from the starter terminals.
4. Remove the starter mounting bolts. Remove the starter. To install:
   
5. Attach the connector to the terminal on the solenoid switch. Connect the cable from the battery to the starter and secure with the nut.
6. Place the starter in the flywheel bellhousing, tighten the mounting bolts to 29 ft. lbs. (39 Nm).
7. Install the air cleaner assembly.
8. Connect the negative battery cable.
9. Check the starter for proper operation.

4A-GE Engine

1. Disconnect the negative battery cable. Remove the both engine under covers.
2. Remove the front exhaust pipe.
3. Remove the electric cooling fan.
4. Disconnect all the wiring from the starter terminals.
5. Remove the starter mounting bolts. Remove the starter. To install:
   
6. Attach the connector to the terminal on the starter solenoid. Connect the cable from the battery to the terminal on the switch and secure with the nut to 29 ft. lbs. (39 Nm)..
7. Install the electric cooling fan.
8. Install the front exhaust pipe.
9. Install the left and right engine under covers.
10. Connec the negative battery cable.
11. Check that the starter works properly.

1. Disconnect the battery terminals from the battery.
Loosen the nut on the NEGATIVE (-) terminal first. You may need to expand the terminal to get it off the post.. you can use a screw driver to gently pry it wider.
2. Disconnect the positive next... same procedure.

3. There is a battery hold-down that needs to be unscrewed. Look down the front edge of the battery. There should be a small plastic or metal clamping plate that is screwed down. Remove the clamp.

4. Carefully lift out old battery,

5. Installation is just the reverse... be sure to attach the positive terminal first..(just for safety's sake)

to help you out..

The problem doesn't need to be the starter; the first thing you should eliminate is the chance that the problem is only poor contact at the battery terminals, the point where the negative cable is attached (either body sheet metal or engine block) and the starter terminal itself.
You can buy a tool for cleaning battery terminals at any auto parts store or, if the battery has side terminals, use any wire brush. - Disconnect the negative terminal from the battery first. - Then remove the positive terminal. - Clean all parts throughly. - Reattach them. - Try starting the engine.
If it doesn't start; - Disconnect the negative terminal again. - From under the car, locate the starter; it will be at the junction of the engine and transmission and it will have one end obviously butted against the transmission housing. - Remove the heavy cable from the starter and clean the cable end and the starter terminal. - Reattach the cable to the starter. - Reattach the negative battery terminal. - Try starting the engine.
If it still doesn't start, it may still be only a drained battery so find someone to 'jump' your battery and try to start the engine again. If it still doesn't start, then the starter could be bad.
I've had pretty good luck with rebuilt starters and these will cost far less than new.