Hi,

here is something to start with:

img = Import["~/Desktop/marker00.jpg"]

First we need a grid. If the boxes are more or less in the same position then we can create a template grid; I used the GetCoordinates tool:

coords = {{80.5`, 321.5`}, {78.5`, 260.0}, {79.5`, 182.5`}, {78.5`, 115.5`}, {80.5`, 51.5`}, {145.5`, 322.5`}, {214.5`, 322.5`}, {281.5`, 322.5`}, {350.5`, 324.5`}, {424.5`, 323.5`}};
Show[img, Graphics[Point /@ coords]]

The dots mark my coordinates. This gives me a coordinate grid:

Show[img, 
 Graphics@Line[{{Min[coords[[1 ;; 5]][[All, 1]]], #[[2]]}, {Max[
        coords[[6 ;;]][[All, 1]]], #[[2]]}}] & /@ coords[[1 ;; 5]], 
 Graphics@Line[{{#, Min[coords[[1 ;; 5]][[All, 2]]]}, {#, 
       Max[coords[[1 ;; 5]][[All, 2]]]}}] & /@ 
  Join[{Min[coords[[1 ;; 5]][[All, 1]]]}, coords[[6 ;;]][[All, 1]]]]

I can extract the relevant coordinate for the x- and y-axes:

xaxis = Reverse@Join[{Min[coords[[1 ;; 5]][[All, 1]]]}, coords[[6 ;;]][[All, 1]]];
yaxis = Reverse@coords[[1 ;; 5]][[All, 2]];

which I can then use to cut the respective fields out. To get a clearer representation I plot them in a grid:

Grid[ArrayReshape[
  ImageTrim[img, #] & /@ 
   Reverse@Flatten[
     Table[{{xaxis[[i + 1]], yaxis[[j + 1]]}, {xaxis[[i]], 
        yaxis[[j]]}}, {j, 1, Length[yaxis] - 1}, {i, 1, 
       Length[xaxis] - 1}], 1], {4, 5}], Frame -> All]

Next, we binaries:

Grid[ArrayReshape[
  Binarize /@ (ImageTrim[img, #] & /@ 
     Reverse@Flatten[
       Table[{{xaxis[[i + 1]], yaxis[[j + 1]]}, {xaxis[[i]], 
          yaxis[[j]]}}, {j, 1, Length[yaxis] - 1}, {i, 1, 
         Length[xaxis] - 1}], 1]), {4, 5}], Frame -> All]

and count the pixels:

graydata = 
 ArrayReshape[
  Total[Flatten[
      ImageData[
       ColorNegate@#]]] & /@ (Binarize /@ (ImageTrim[img, #] & /@ 
       Reverse@Flatten[
         Table[{{xaxis[[i + 1]], yaxis[[j + 1]]}, {xaxis[[i]], 
            yaxis[[j]]}}, {j, 1, Length[yaxis] - 1}, {i, 1, 
           Length[xaxis] - 1}], 1])), {4, 5}];

We can plot this to check:

graydata // ArrayPlot

There are obviously two clusters:

clusts = FindClusters[Flatten[graydata], 2];

Which we can use to attach a "1" to "ticked" and a "0" to "unticked".

Flatten[Table[# -> 2. - i & /@ SortBy[clusts, Total][[i]], {i, 1, 2}]]

That gives us the matrix we want:

Grid[graydata /. Flatten[Table[# -> 2. - i & /@ SortBy[clusts, Total][[i]], {i, 1, 2}]], Frame -> All]

Note, that this describes the train of thought. We can wrap everything up into this nice and easily readable function:

tickedBoxes[img_Image] := 
 Module[{}, 
  coords = {{80.5`, 321.5`}, {78.5`, 260.0}, {79.5`, 182.5`}, {78.5`, 
     115.5`}, {80.5`, 51.5`}, {145.5`, 322.5`}, {214.5`, 
     322.5`}, {281.5`, 322.5`}, {350.5`, 324.5`}, {424.5`, 323.5`}};
  yaxis = Reverse@coords[[1 ;; 5]][[All, 2]]; 
  xaxis = Reverse@Join[{Min[coords[[1 ;; 5]][[All, 1]]]}, coords[[6 ;;]][[All, 1]]];
  graydata = ArrayReshape[Total[Flatten[ImageData[ColorNegate@#]]] & /@ (Binarize /@ (ImageTrim[img, #] & /@ 
         Reverse@Flatten[Table[{{xaxis[[i + 1]], yaxis[[j + 1]]}, {xaxis[[i]], yaxis[[j]]}}, {j, 1, Length[yaxis] - 1}, {i, 1, Length[xaxis] - 1}], 1])),{4, 5}]; 
  clusts = FindClusters[Flatten[graydata], 2]; 
  graydata /. Flatten[Table[# -> 2. - i & /@ SortBy[clusts, Total][[i]], {i, 1, 2}]]]

If you throw your image in it should work:

tickedBoxes[img]
(*{{0., 1., 0., 0., 0.}, {0., 0., 1., 0., 0.}, {0., 1., 0., 0., 0.}, {0., 0., 0., 1., 0.}}*)

There is a lot we can improve, but it should be a starting point.

Cheers,

Marco