Have you tried to clear memory prior to running the first FEM matrix? It maybe that the second works because kkk has had no prior remembered definitions. Try after including the Clear statement before your definition for kk.

Clear["Global`*"]

Strange, this works here

In[20]:= (* http://community.wolfram.com/groups/-/m/t/352651 *)
Clear[a, iy, l, e, kk]
kk[a_, iy_, l_, e_] := 
 {{e a/l, 0, 0, -e a/l, 0, 0}, 
  {0, 12 e iy/l^3, 6 e iy/l^2, 0, -12 e iy/l^3, 6 e iy/l^2}, 
  {0, 6 e iy/l^2, 4 e iy/l, 0, -6 e iy/l^2, 2 e iy/l}, 
  {-e a/l, 0, 0, e a/l, 0, 0}, 
  {0, -12 e iy/l^3, 6 e iy/l^2 , 0, 12 e iy/l^3, -6 e iy/l^2}, 
  {0, 6 e iy/l^2, 2 e iy/l, 0, -6 e iy/l^2, 4 e iy/l}}

In[22]:= Dimensions[kk[Sequence @@ Range[4]]]
Out[22]= {6, 6}

In[23]:= kk[Sequence @@ Range[4]]
Out[23]= {{4/3, 0, 0, -(4/3), 0, 0}, {0, 32/9, 16/3, 0, -(32/9), 16/3}, 
          {0, 16/3, 32/3, 0, -(16/3), 16/3}, {-(4/3), 0, 0, 4/3, 0, 0},
          {0, -(32/9), 16/3, 0, 32/9, -(16/3)}, {0, 16/3, 16/3, 0, -(16/3), 32/3}}

In[25]:= N[MatrixExp[kk[Sequence @@ Range[4]]]]
Out[25]= {{7.69596, 0., 0., -6.69596, 0., 0.}, 
          {0., 1.3434*10^8, 1.18394*10^8, 0., -1.3434*10^8, 2.14073*10^8}, 
          {0., 2.01511*10^8, 1.77591*10^8, 0., -2.01511*10^8, 3.21109*10^8}, 
          {-6.69596, 0., 0., 7.69596, 0., 0.},
          {0., -2.8509*10^7, -2.51245*10^7, 0., 2.8509*10^7, -4.54298*10^7}, 
          {0., 2.01511*10^8, 1.77591*10^8, 0., -2.01511*10^8, 3.2111*10^8}}

things you could try

• clear variables like the example does (has been already said earlier here)
• start Mathematica new, open an new notebook and copy the above expression into it ...
• do you use special contexts or do you enjoy some outrageous formatting rules or language settings in your operating system showing you other symbols in the FrontEnd than send to the kernel??
• if it denies still to work, give FullForm[] a try to see what is send to the kernel ...

This evening I had the following error

which seemingly is meaningless. But I had used the escape key careless (to insert the \[Mu]). After reediting the extra-escape disappeared and the code became legal. Thereofore I'm afraid in your case some non-printable (and wrong) key strokes in connection with 2D-input caused the error.