An additional reason for removing the batteries from any device that will not be used for a while - as long as there is a battery in the device, there is a voltage present that can "accelerate" the corrosion of the battery contacts (and anything else nearby).
The process is similar to "electroplating" except that you "plate" the battery contacts with whatever crud happens to be in the air.
Most of the corrosive products that are likely to accumulate in this way are not particularly good conductors. The result is that when you "pull" current, the voltage seen by the equipment drops - even though the battery itself may be fully charged. This could be the cause of the "static." The current pulled by the recorder varies with what it's doing, and the voltage varies (probably non-linearly) with the current draw.
If the crud isn't too bad, wiping the terminals may suffice. If it gets bad enough to penetrate the terminal plating, you can expect to have continual problems with erratic voltage to the device.
If the capacity of a rechargeable is significantly reduced, it is sometimes possible to restore it somewhat by "reforming." This usually involves a complete discharge and recharge cycle. With "battery packs" containing multiple cells, however, this may be difficult. Unless each of the individual (internal) cells can be brought to zero charge at the same time reforming doesn't work very well.
If your electronics supplier can't get you a replacement, you might find something suitable from a cell-phone shop(?), although you'll probably need to do your own matching of specs.