I have a Western Digital 160 GB External USB 2.0 HDD (Model #
WD1600B008-RNN). It was working well and good and suddenly it stopped
working when I wasnt around. My brother was using it and he says he may
have changed the polarity for the DC input. I had a DC adapter which
can accomodate multiple heads. I changed it to right polarity and
switched it on.

When I switch it on, both the green and red lights are always lit, PC
identifies that there is a USB device connected, but it cannot "see"
the Ext HDD. Windows Drive Information did not list this drive.

I tried with WD Data Lifeguard Diagnostic for Windows program that lets
the PC to identify the drives but the drive did not show up. I tested
the input power cable and it is working.

I suspect there is a board failure as the DC polarity was mixed up.
Since I dont work much on storage hardware, I suspect that there should
be a control mechanism/fise which may prevent the board/hard drive from
being fried.

There is not. Not for this type of failure, since it is rather hard to
protect semiconductors against it, when you cannot afford a
signifivant voltage level drop (0.5V) on the power lines. The only
way that works would require power isolation and wide-range inputs on
all logic lines. Possible, but expensive. Nobody does it.
If you can afford that voltage drop, a rectifier diode on 5V and
12V input cpuld be used. The logic input protection would
still be needed, since otherwies the ESD circuitry can fry itself.
Nobody does this either.

It seems that OP (or his brother) used a diiferent AC adapter then
originally supplied with his external disk.
Accidents happen.....
Most of them create some damage. Life is a learning process.

So what would be the next logical step for trouble shooting ??

Think about what the data is worth. If it is enough, then contact
a professional recovery service. Otherwise throw the drive away,
there is nothing you can do.