Below are some techniques that together with @nikie answer give you a powerful way of detecting specific table grids.

The Rubber Band Algorithm

The 3 columns to be detected must be very close to 40%, 15% and 45% of the total table width. Similarly, the line heights have a proportion to follow. So the first problem to solve is how to identify a sequence that matches a proportions pattern.

I first tried to look for a Mathematica built-in function as this is a very generic task. The closest I could find is the SequenceAlignment function but it work only on strings. So I developed my own algorithm which is explained in this video

This is how I implemented it:

rubberBandComparePair[wanted_List, suspectsSubset_List] :=
  Module[{rubberBand, reducedSuspects},
    rubberBand = Rescale[wanted, 
                         { Min@wanted        , Max@wanted         },
                         { Min@suspectsSubset, Max@suspectsSubset }];
    
    reducedSuspects = If[Length @ rubberBand < Length @ suspectsSubset, 
                         Flatten[Nearest[suspectsSubset, #] & /@ rubberBand],
                         suspectsSubset];
    
    {EuclideanDistance[rubberBand, reducedSuspects] /
     (Max@reducedSuspects - Min@reducedSuspects),
     reducedSuspects}
  ] /; Length@wanted <= Length@suspectsSubset


rubberBandCompare[wanted_List, suspects_List] := 
  Module[{w, k = Length @ wanted, costs, sortedSuspects},
    sortedSuspects = Union @ Sort @ suspects;
    w = Length @ sortedSuspects;
    costs = Flatten[#, 1] & @ 
      Table[rubberBandComparePair[wanted, sortedSuspects[[start ;; end]]],
            {start, 1, w - k + 1},
            {end, start + k - 1, w}];
    SortBy[costs, First][[1]]
  ] /; Length @ Union @ suspects >= Length @ wanted

rubberBandCompare[wanted_List, suspects_List] := 
{∞, {}} /; Length[Union@suspects] < Length[wanted]

For example if we are looking for a sequence proportional to {1,2,4} in the list {9, 10, 15, 21, 40, 55}:

In[1] = rubberBandCompare[{1, 2, 4}, {9, 10, 15, 21, 40, 55}]
Out[1] = {1/30, {10, 21, 40}}

and we have detected that {10,21,40} matches {1,2,4} with an error of 1/30. Notice that this error is a relative error that does not change with scale:

In[2] = rubberBandCompare[{1, 2, 4}, {90, 100, 150, 210, 400, 550}]
Out[2] = {1/30, {100, 210, 400}}

Detecting horizontal and vertical lines

In order to detect lines we can use ImageLines[] or we can use the lower lever Radon[]. The advantage of ImageLines is that it is fast and simple, but it always looks for lines in all directions whereas Radon lets you look for lines in a specific direction. I implemented solutions using both, but I'll explain here only the ImageLines[] solution which worked well in a large number of cases.

ImageLines returns a list of lines where each line is defined by 2 points. So we first write this very simple function to calculate the angle of a line:

lineAngle::usage = "lineAngle[{{x1,y1},{x2,y2}}] returns the angle of the line that goes
                    through points {x1,y1} and {x2,y2}.";
                    
lineAngle[{{ x_?NumericQ, y_?NumericQ},{x_          , y_          }}]:=Indeterminate
lineAngle[{{ x_?NumericQ,y1_?NumericQ},{x_          , y2_?NumericQ}}]:=Pi/2
lineAngle[{{x1_?NumericQ,y1_?NumericQ},{x2_?NumericQ, y2_?NumericQ}}]:=ArcTan[(y2-y1)/(x2-x1)]

When we call ImageLines later on, it will return a list of lines, so we need a function to select the ones that are close to the desired direction. For this I wrote this function:

selectLinesNearAngle::usage = 
    "selectLinesNearAngle[{{{x1,y1},{x2,y2}},...}, angle, tolerance] \
     selects the lines that have an inclination of angle +/- tolerance. \
     Each line is defined by a pair of points.";

selectLinesNearAngle[lines_List, angle_?NumericQ, angularTolerance:(_?NumericQ): 4°] :=
  Select[
    lines, 
    Or @@ Thread[Abs[lineAngle[#] - angle + {-Pi, 0, Pi}] < angularTolerance] &]

Now we are ready to write our modified version of ImageLines for horizontal or vertical lines:

Options[angularImageLines] = {"Debug" -> False};

angularImageLines[img_Image, α_, OptionsPattern[]]:=
  Module[
    {lines, selectedLines, binarizedImage},
    binarizedImage = Binarize@GaussianFilter[img, 3, Switch[α, 0, {2,0}, Pi/2, {0,2}]];
    lines = ImageLines[binarizedImage];
    selectedLines = selectLinesNearAngle[lines,α];
    If[OptionValue["Debug"],
       Print[Show[binarizedImage, Epilog -> {Green, Line /@ selectedLines}]]];
    selectedLines
  ]/; α==0 || α==Pi/2

Notice that binarizedImage is using GaussianFilters as @nikie recommends. This is an example of how it works:

Searching for the lines that match wanted proportions

It is now the time to use rubberBandCompare and angularImageLines together:

matchedLines[wanted_List, g_Image, α_] := 
  Module[
    {candidateSequence, suspects, error, bestMatch, lines}, 
    lines = angularImageLines[g, α];
    suspects = Sort[Switch[α, Pi/2, First, 0, Last] /@ ((#1[[1]] + #1[[2]])/2 & ) /@ lines]; 
    candidateSequence = rubberBandCompare[wanted, suspects]; 
    If[Head[candidateSequence] === rubberBandCompare, Return[$Failed]]; 
    {error, bestMatch} = candidateSequence;  
    If[α == Pi/2 && error > 0.01176495, Return[$Failed]];
    If[α == 0    && error > 0.02994115, Return[$Failed]];
    (Cases[lines, {{x1_, y1_}, {x2_, y2_}} /; 
     Switch[α, Pi/2, (x1+x2)/2, 0, (y1+y2)/2] == #1, 1, 1][[1]] & ) /@ candidateSequence[[2]]
  ]

Notice that the error needs to be lower than a calibration constant for the solution to be accepted. These constants are found using a set of sample files, and making a histogram of the errors.

This is an example:

Lines Intersections

This function finds the intersection of two lines. It was found in the PlaneGeometry.m package by Eric Weisstein (see http://mathworld.wolfram.com/Line-LineIntersection.html):

Intersections[Line[{{x1_, y1_}, {x2_, y2_}}], 
              Line[{{x3_, y3_}, {x4_, y4_}}]] := 
  Module[
    {d   = (x1-x2) * (y3-y4) - (x3-x4) * (y1-y2), 
     d12 = Det[{{x1, y1}, {x2, y2}}], 
     d34 = Det[{{x3, y3}, {x4, y4}}]}, 
    If[NumericQ[d] && d == 0., 
       PointAtInfinity,
       {Det[ {{d12, x1-x2}, {d34, x3-x4}} ]/d, 
        Det[ {{d12, y1-y2}, {d34, y3-y4}} ]/d}]
  ]

Uniformize Background

This technique is explained by @nikes here. I just added the /.0. -> 0.0001 in order to avoid division by zero when large pure black areas are present:

uniformizeBackground[g_Image] := Image[ImageData[g]/(ImageData[Closing[g, DiskMatrix[5]] /. 0. -> 0.0001)]

Grid Centers

gridCenters[g_Image] := 
  Module[
    {gAdjusted, hLines, vLines, 
     wantedX = {16.5, 224.5, 302.5, 535.5}, 
     wantedY = {22.5,  50.5,  97.5, 125.5, 154.5}}, 

    gAdjusted = uniformizeBackground[g];
    {hLines, vLines} = {{wantedY, 0}, {wantedX, Pi/2}} /. 
                {wanted_List, (α_)?NumericQ} :> matchedLines[wanted, gAdjusted, α, opts]; 
    If[hLines == $Failed || vLines == $Failed, Return[$Failed]]; 
    Outer[Intersections, Line /@ hLines, Line /@ vLines]
  ]

The wantedX and wantedY are found from a sample image using the get coordinates tool from the drawing tools palette. Once we have the grid centers, we can use the same techniques that @nikie used to identify and straighten any of the cells.

This is an example:

A final comment

My main contribution in this answer in the rubberBandCompare function which useful to other people in other areas. If it was already invented somewhere else, please let me know.