If the board turns on with the charger connected but then dies the moment it is removed, then the batteries are too discharged to be charged. Lithium Ion batteries have a condition where when left for long period times they discharge to a level that they cannot be charged,
If you do not put the spudger in so deep as to damage the seal you do not need to replace it. Also, you do not need to remove the whole internals to replace the battery, if you disconnect the battery cable after removing the two #00 philips the battery and circuit board pivot open. Here is someone doing this same repair as I describe.