When a camera formats a card it wants control of that card. It something else changes the card the first camera will think the card is corrupted and in a way it has. Cards are not that expensive. Please use one card in one camera and back up you files on a computer.. I have found NO problem with deleting folders on my cameras using the computer. You typically can REMOVE photos on a COMPUTER you should ONLY let the camera ADD photos. use one Card for one camera.
Your battery is most likely dead, you will need to purchase a new one. Here is a link for one to buy on Ebay.
You don't. There are special tools and a lot of training required to do anything inside a modern digital camera. It is densely filled with flat wire cables, tiny screws and parts that will fill a drinking glass. If you do take it apart, you'll never get it back together. What do you expect to accomplish?
The best way to transfer pictures from your camera to your computer involves removing the memory card from the camera and plugging it into a card reader (either built-in to the computer or connected via USB). This is likely to be faster than connecting the camera to the computer, and won't run down your camera's batteries.
Once the card is plugged in, it will appear to your computer as a removable drive. You can use the operating system's drag&drop facility to copy pictures from the card to the computer's hard drive, the same way you copy any other files. Or you can use Nikon Transfer or any other photo management program such as Picasa. Organize edit and share your photos
Let's start with your battery. It could be bad, the camera's charging circuit could have failed or the electrical contacts on the battery or in the camera could be dirty.
Start by cleaning the contacts. I find that a clean pencil eraser works quite well. If that does not work, consider the age of your battery. Rechargeable batteries do not last forever. They are rated for a certain number of charge/discharge cycles and they may or may not meet the specification. Your battery could be old and cannot hold a charge; in which case you need to buy a new EN-EL5 battery.
The other possibility is that the charger circuit in your camera is not longer functional. If it has gone bad, the cost of repair might not be justified. Instead, I would buy an external charger. The Nikon battery charger you need is model MH-61. Nikon's price is $27.95, but you can probibly find one for less.
I the file is on your computer, it means your folder is empty and there are no images or other files in it. If it says "no Image" on your camera, it simply means you have a blank memory card, or possibly "no" memory card in the camera.
Did you charge the battery correct? Was the power light on the camera blinking while charging? Did it take about or less than 3 and a half hour tho charge? Please also check if all contacts o the battery and in the camera are clean and shiny. To clean the contacts, only use dry cloth and / or cotton swabs. Also make sure the battery-chamber/ memory card slot cover is closed correct. There is a switch detecting an open door. As long as the door is open the camera won't start.