I have a Nikon 4600 which I use constantly. It suits my needs perfectly but the door of the battery compartment is broken and it's only a matter of time before it comes off. I would like to mend it but can't afford to pay a lot. Could I order the part and do it myself?

sir,
this part is available with Nikon agency, to replace this you have to open the whole camera, then detach the front portion, it doesn't matter, just a piece of rubber or sponge fix on the battery lid, this will be help full to hold the battery at contact perfectly.

Always be sure the batteries are charged and suited for your device.
Check contacts of the batteries and in the battery compartment of your device. Dirty or oxidised contacts can be cleaned with a dry cloth, or a cotton swap. Never use sharp tools to clean contacts or anything sharp in or on electronic equipment.
Always charge batteries before using it for the first time, or if you have not used it for a long period. 3 months is a very long period.

Also check if the battery door is closed correct. there is a switch connected to the battery door. If the switch does not work correct, it could be you can't switch on your camera.

hiwould you show the broken area? you can post picture the broken area if you have extra camera. there is one thing you should check battery door hook, post, and battery compartment area. please make sure what really broken then I can help

You can order the battery compartment door from
http://uscamera.com/636-082-3877.htm

http://uscamera.com/636-082-3877.htm

On the bottom of the camera you'll find a plastic tripod mount and the battery compartment. The door covering the battery compartment is fairly sturdy, and it has a locking mechanism. As you can see, the Coolpix 4600 and 5600 use two AA batteries.

http://uscamera.com/636-082-3877.htm

Mine has broken as well. It appears this clip is just to keep the battery from falling out as you open the battery door. It will function perfectly fine without the clip. Just be careful not to drop the battery when you open the battery compartment.

Hope this helps,
-Tor

Go to store and purchase a memor card reader/writer. It will allow you to put your memory card in it and download the pictures to the computer via the usb port. Make sure the reader/writer is made to accept your type of memory card.

Call 3104148107 This is the Nikon Parts line, be warned it will probably take as long as 30-45 minutes of old time to get to a person. 
Once you can get to a person, give them the camera model and describe the problem. They just sold me a replacement battery door for $9.95 + $6 dollars shipping and handling. 

The rep was so nice he even printed out the device design blow up, and the relevant section of the manual, so I could see the step by step with out having to purchase the full blown repair manual, which runs $83.