The “battery” on the PCB looks like a typical battery, but it’s actually an ultracapacitor, charged by the system battery, that maintains the device clock when the removable battery pack is removed.
If you have corrosion/leakage around it, the electrolyte may have leaked. I have run into clock issues before on these machines, but the culprit is the oscillators, and not the wee cell. The ULP clock uscillator is a wee chip next to the CPU, a flat device that clocks at 32kHz. When the Sansa is powered off, this device maintains the clock and the required secure clock used for DRM capability. The main oscillator device is larger, the system clock chip. This one is active when the Sansa is on and playing music.
Do you have multiple music files that play incorrectly? Typically, we’re dealing with 44.1 or 48kHz sample rates, both of which the Sansa understands.
The v1 device uses the same, or a very similar, “button” device. One can be salvaged from a dead v1 Sansa (you’ll note that the PCB is radically different, with a much higher device count on the board. The v2 is quite simpler. The biggest hurdle to overcome with PCB repairs involving the v2 e200 Sansas is their rarity, as there are many times more v1 machines out there.