My battery is way up front under the fuel tank. However, there is a connector coming from the on/off switch which is accesible. Is this connector meant to charge the battery with?

If charging with that connector, does it matter what position the switch is in?

Also, I think we left the power switch on after my last flight yesterday, even though the radio was off, and this morning, nothing works. Will the battery discharge when the power switch is left on?

You are correct, that is the charging connector

The switch must be off. Most chargers have an LED that will be on when it is charging

Yes, If you leave the power switch on in the plane, it still will discharge the battery as the reciever and servos will be using power. Try not to do this as this can cause receiver damage if done often enough. I personally have never seen this, it's just what I have been told. I do know that you definitely do not want to do that with the radio as it can burn up the output circuit. I have seen that first hand.

Yes, it is for charging and testing the voltage of your battery. Hopefully you have a battery tester. On most of my planes I use a switch holder, such as this one: http://www2.towerhobbies.com/cgi-bin...?&I=LXJ778&P=0
I like these, or ones like it, because they move the switch inside the plane, which protects it a bit better from exhaust, and put the charge jack in a convenient place for charging and for testing the voltage at the field.
Yup, it matters. It is dead when the switch is on. You can see this by hooking the battery tester to it and switching on an off. You can also see if you've got the charge connector hooked to it, the little light will go on and off.
Most definitely. Even though the servos are not moving, the receiver and servos are using a small amount of electricity. Charge the battery and then measure the voltage to confirm the battery is ok.

Think of the swtich as directing the battery to one of two leads, the one that goes to the receiver, or to the other one, which you can use to charge and test the battery. One of the two is always "live", as mentioned above.

As for running the pack all the way down, I've done this more times than I care to count. I've had packs "come back", and show no damage, and I've had packs damage a cell and become garbage from this. So, you really should test out the pack after a charge. Get it on the charger for about 20hrs at the "wall wart" rate. Testing the pack after this requires either a loaded volt meter, or a cycler. A cycler is better, but you can make due with a properly loaded meter.

A loaded meter is basically a meter that puts a resister accross the battery to drain some current. If you juse a regular voltmeter like you'd find at radio shack, you get a falsely high reading. Meters made for the hobby usually have a load built in, or you can wire up a load yourself (not going in to "how" here to save space).

Test the pack right off the charger. Most 4.8v Nicads will show 5.0-5.3volts. Anything less than 4.9 is probibly a bad pack. Now, turn the plane on and wiggle the sticks for about 10min. That's to take off the top of the charge. Now, switch off and check the battery voltage with the meter. You should show at least 4.8volts, preferably higher. If it's showing less than 4.7, it's very much toast. Even 4.7 after 10min of non-flying loads would have me tossing the pack. A good pack should still be over 4.8 at this point, so if it's only 4.8, the pack is marginal, and you'd want to replace it or at least do some cycle testing to find out what capacity it has left, and monitor is closely in the future.

Remember, batteries are cheaper than airplanes. When it doubt, toss the pack. A new $15 pack could be money well spent.

Pay attention to what Montague wrote about your pack. Although when I've left packs on they've usually come back, it's not always the case, and you don't want to lose your new plane becasue your pack went bad.

By the way, the "loaded" voltage meter, also called an "Expanded Scale Voltmeter" (ESV) can be bought at Tower or most Hobby Shops for under $20 and is the best investment you can make in this hobby. Use it to test your pack after every couple of flights.
Dennis-

Piper Chuck... I've got some of those that you mentioned but I dont' think they are that easy to use. Although they are pretty with the aluminum finish on the switch, the charge isn't so easy to use. I would recommend something like this, which I've used with great success. It's slightly unsightly but much easier to use. Mine had a larger switch with a protective shelf to prevent accidentally turning it off but didn't have the LED lights. I have used it on several planes. It currently resides in my Lazy Tiger.