Kirchhoff's Laws help

[vaio911]

Homework Statement

Find $i_1,i_2,v_A,\text{ and }v_H$ in the ladder network. Calculate the power dissipated in the $2\;\Omega$ resistor.

http://i.snag.gy/PIhxl.jpg

Homework Equations

Kirchhoff's Laws (i.e. current law, voltage law).

The Attempt at a Solution

Ok, I know that I can simplify the circuit down to one loop then use Ohm's law to calculate $i_1$, but then I have to do other things to get the other stuff.

I tried to make a system to solve this problem using the laws.
Can somebody tell me where I'm doing wrong here?

$\begin{align} i_b&=i_c+i_a\\ i_c&=i_e+i_d\\ i_e&=i_g+i_f\\ 12i_a-28+8i_b&=0\\ 12i_a+6i_c+15i_d&=0\\ 4i_e+10i_f+15i_d&=0\\ 2i_g+13i_h+10i_f&=0\\ 4i_e+2i_g+13i_h+15i_d&=0 \end{align}$

Getting me something like:
$-\frac{7}{39},\frac{49}{13},\frac{154}{39},\dots$

which I know is completely off.

 

[vaio911]

If you can't understand my handwriting,

$V_a$ is the one w/ the 12 ohms.

$V_h$ is the 13 ohms one.

 

[vaio911]

It is because of the direction of the currents?

 

[CWatters]

I'd probably just simplify it. If you keep your working for each step it will help when it comes to working out the voltages using the potential divider rule.