ResistanceMatrix[g_Graph] := With[{n = VertexCount[g], km = KirchhoffMatrix[g]},
  Table[ ReplacePart[ Diagonal[ DrazinInverse[ ReplacePart[km, k -> UnitVector[n, k]]]], k -> 0],
  {k, n}]
]

rm = ResistanceMatrix[GridGraph[{10, 10}]];

N[rm[[12, 68]], 40]