What happens with these batteries?
It seems as if the small NiMH varta batteries are starting to give up the ghost. Normally this would not be a big problem, but these batteries begin to leak chemicals in the early stages of retirement, as seen below.

If you have not opened your sealed Doj or checked your battery, it is ESSENTIAL that you do it now! Your battery WILL leak, it is only a matter of when, not if.
How can I prevent this?
Replace or remove your stock battery, even if there is no visible sign of leaking or crystals forming. Note: You can only remove the battery on a normal (non Black Label) Doj safely. BL boards will suicide without a working battery. Once a new battery is installed, continue to keep an eye on it. I check mine about once a month. These batteries will last about 5 years, but it's better safe than sorry when you are talking about a $400+ game. Do NOT keep your Doj PCB's seal intact just because you are a collector, your board WILL die as a result, and repairs will be difficult if not impossible.
My battery is corroded, but my game still works. What now?
There is still time to prevent any further damage. Unfortunately, when the battery has crystals on it, this means the chemical compound has already started to leak onto the board. You need to remove the battery immediately. I recommend desoldering the battery, but if you aren't savvy with a soldering iron, cut off the battery.
After you remove the battery, you need to make sure that any corrosive chemicals on your PCB are neutralized. This step is important, and should be performed as a preventative measure.
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After performing this, clean the area thoroughly with a damp paper towel, then dry. Do not power on your PCB until you are certain that it is dry. I usually wait about 12 hours.
My battery is corroded, and my game is no longer working.
This means the chemicals have already started to corrode the components or traces on your board.
Does the game need the battery to function properly?
For standard non-Black Label DOJ PCBs, the answer is no. The battery only retains the soft dip settings. Without the battery, your game will reset to default settings on each power cycle.
I will be adding more to this post.