Why do the batteries pop out of the QC-906 battery charger?

Send it to a camera repair shop. Disassembling the lens is not an easy job.

No. You need a separate battery charger, such as http://www.overstock.com/Electronics/BasAcc-Battery-Charger-Set-for-NP-45-Fuji-FinePix-S610-J110-J150W/7124327/product.html?searchidx=3

The JX-400 is a camera, not a battery charger. Connecting it to a computer's USB port simply drains the battery faster since the camera has to expend juice communicating with the computer (even if only to say it has nothing to say).

One source for a battery charger is http://www.overstock.com/Electronics/BasAcc-Battery-Charger-Set-for-NP-45-Fuji-FinePix-S610-J110-J150W/7124327/product.html?searchidx=3

The Nikon D40 uses the EN-EL9 7.4 Volt Li-ion Battery. You should be able to read 7.4 V DC between the (+) & (-) terminals of the battery after it has been in the charger for several hours. If it does not, it indicates a bad battery, charger or both. There should over 7.4 V DC on the terminals of the charger if there isn't, it suggests a bad charger. If the battery voltage is OK, make sure it is inserted correctly. If still having trouble, it may be related to the camera power switch or internal circuitry. This will require returning to Nikon for repair. Good luck!

Your battery probably is in the wrong way.So take it out and look on the bottom of it.You will see 3 copper cubes.Next look in to the slot where the battery goes and you will see 3 metal wires.Now take your battery and carefully line up the copper slots with the metal wires.Then push the battery in and close the battery slot.And your done go plug it into your USB slot and you will see a white battery symbol and you will know that it is charging.
Simple fix for a simple problem.

Just because someone claims a battery is compatible does not make it so. Nikon knows the specs of their batteries. Third-parties have to reverse-engineer to work out the specs, and they don't always get everything right.
Stay with Nikon batteries, unless you want to jeopardize your camera just to save a few dollars.

Read page 16 of the manual. Do not use any other charger with this camera. Are you sure you have the battery inserted correctly? When trying to charge, does the green light blink? If so, when it stops blinking and turns off, the battery should be fully charged. Do not attempt to turn the camera on while the charger is trying to charge the battery.

No. The NP-45A battery needs a separate charger. If you need a charger, one source is
http://www.overstock.com/Electronics/Battery-and-Charger-for-Olympus-Li-40B-Fuji-NP-45/6042413/product.html

http://www.overstock.com/Electronics/
Battery-and-Charger-for-Olympus-Li-40B-Fuji-NP-45/
6042413/product.html

Charger flashing red indicates the battery is still not full and is in the process of recharging.
Red light steady indicates your battery is fully charged and ready to operate with your Coolpix 5000.
When red light is off it indicates there is no battery inserted or the charger is not pluged in.

Hello,
A. Have you checked these first?
1. Is the battery correctly inserted?
2. Is the battery in correct orientation?
B. May be your battery fabrically is not NORMAL.
Your battery NP-45 must be checked. You should control and be sure that your battery is in good condition.
1. You may do it by this way:
You can do it practically by going to the nearest store and take a new battery from there for only checking. When you go to the store please want a permission from them to check your battery. It only takes a minute. When you place a new battery to your BC-45B charger. If the led turns yellow or green but your battery does not do the same then it means your charger is in good condition but your battery is out of order.
2. Also you may do it by another way.
Check your battery with a multimetre if have one and know how to use it.
C. Please buy a new battery and replace with your old one. I looked on internet for you where you can buy from a chipest and a trusted place. On ebay.com it is sold. Please open ebay.com and write on the seach box 370357190515. It is sold from a trusted seller with shipping FREE.
I think your problem will be solved by changing your battery with new one.
If your problem is not solved. Please feel free to contact me again.
Best Regards