This is a general answer rather than specific to the D200.
If possible obtain another battery that works OK in another camera.
Also, if possible, it may help to have access to a D200 that does not have this problem.
Try the 4 possible combinations of G (good) and F (faulty) for body and battery (GG GF FG FF), see how they compare and try to see what makes some work and some not.
Also, you are starfing out with FF (Faulty body, faulty battery).
eg if GF works and FG (Faulty body, good battery) still doesn't then the issue is more likely to be with the body than the battery.
Look carefully at how the battery is intended to be retained and try to see what is wrong with the system. This may be due to wear or breakage of a latching part of due to dirt or other debris trapped in part of the system - either in the battery of the camera.
I have seen batteries which have accumulated an apparently minor amount of "debris" in slots in the battery-body. Cleaning this out has restored correct action. A wooden toothpick (or several) is often a useful cleaning aid as it will not damage hard plastic or most battery contacts if used sensibly.
It's possible that there are spring loaded contacts that the battery is pressed home against and that these have lost their "set" and are more depressed than they should be. Springs can often be "restretched" but, this should be done if at all by someone who has "some clue" about the process.