The principal difficulty is that the backup battery, which allows graceful shutdown and preservation of the contents of memory when the system battery is close to exhaustion, does not itself begin to recharge after it has been exhausted during storage before the system battery has reached close to working voltage again. Otherwise, only leaving the PB on the adapter for anything up to a week is likely to get enough charge (30-50mAh) into the backup for a return to quasi-normality of power management, and even that may not work if the system battery is beyond recall. In your case, with new cells in the system battery, there may be a better outcome.

It is unlikely that the backup (which is a secondary rechargeable cell, not a primary cell as in desktops, and very rugged in my experience) is itself unserviceable.

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