Calculating Thevenin voltage and Norton current for complicated circuit
First, Try redrawing the circuit, and label all the nodes, giving letters to the unknown ones and values to the known ones. Choose a 0V node:







simulate this circuit &ndash; Schematic created using CircuitLab

From this, you can tell that a is always 5V.

You can then set up a system of equations for each case. First, for the open circuit case, we can say that:


Vo=Va-Vb=5-Vb
Io=0
V2=2*0=0
Vc=5+0=5V
Ir1 = Vc/1=5/1=5A


We now need to figure out the current I1. we can say directly that:


Vb = 10 - Ir3*2


The current through R3 is the sum of the current through R2 and the current through I1. Both of these currents directly depend on Vb.


Ir3 = Ir2 + I1
I1 = 2*(Vo) = 2*(Va-Vb)=2*(5-Vb)
Ir2 = Vb/4


We now can solve for Vb:


Vb = 10 - Ir3*2 = 10 - ((Vb/4) + 2*(5-Vb))*2
Vb = 10 - Vb/2 - (20 - 4Vb) = 3.5Vb  - 10
0 = 2.5Vb - 10
Vb = 4V


Now lets check that this works. If Vb = 4V, Vo = 1V, so I1 = 2A, so Ir3 = 2 + 4/4 = 3A. 3 amps through a 2 ohm resistor (R3) drops 6V, and 10-6 = 4V, meaning that we were correct.

You can do a similar procedure for the short circuit current. 

It's probably faster to use superposition, but it's a bit more mathsy and slightly less obvious.