If Tamil Nadu breaks up from rest of India......

What will happen if Tamil Nadu state breaks up from India to form an independent country ?

Summary: A breakup would be terrible for both Tamil Nadu and India. 

Disadvantages for Tamil Nadu:

1. Tamil Nadu is a dry region that depends on water from the neighboring 3 states of Karnataka, Kerala and Andhra Pradesh. By going separate, we will make the water disputes go international. The negotiations for water sharing will be harder.
2. Tamil Nadu will have a pretty weak army. Although we Tamils used to be strong fighters in the distant past, in the present time we are not a warring group. Tamils form a small portion of present Indian army (usually dominated by the Sikh and Gorkha regiments).
3. If Tamil Nadu had broken away from India, I presume that the relationships between these two nations would be cold (similar to India-Pakistan). The relationship with Sri Lanka would be even worse (the new TN would be emboldened to interfere more in SL) Given the geography, TN would have to depend a lot on India & Sri Lanka for a lot of its necessities. We will have two hostile neighbors, with no friends in the geographical vicinity.
4. Given 2 & 3, we will spend most of our time in wars, but not always in the winning side.
5. Tamil Nadu will have to find newer ways to generate electricity. Currently, we get a lot of electricity from Central government funded projects. Although there is scope for wind & solar and some lignite, for everything else we need the support of rest of India.
6. Tamil Nadu is rich in a few minerals such as the lignite, graphite and phosphates, but pretty poor when it comes to critical resources such as oil, natural gas, iron ore, bauxite.
7. Tamil Nadu is not self-sufficient when it comes to food and imports a lot of food from other states (from AP mangoes to Punjab rice).
8. Most of software product related jobs and other well paying jobs are outside Tamil Nadu. You would then need a visa to go and work in Bangalore, Hyderabad, NCR or Mumbai.

Disadvantages for rest of India:

1. Tamil Nadu is the largest when it comes to the most literate states and a break up of TN will pull India's literacy rate & Human development indicators down.
2. Tamil Nadu has the highest number of business enterprises in the country (one-ninth of all Indian businesses are from here)[1], the most urbanized state, second biggest software services exporter and the 4th biggest by GDP. India's economic output will suffer.
3. India will have one more hostile neighbor and that will put even more strains on the defense.
4. Tamil Nadu forms one of the core manufacturing bases for India (along with Maharashtra and Gujarat) and losing would push back our national interests significantly.
5. India will lose the two critical ports of Chennai and Tuticorin. That will affect the international trade and capabilities of the Navy.
6. Tamil Nadu receives the maximum number of foreign tourists [2] and without this, there will be a drop in India's tourism revenues.

Overall it will be a lose-lose proposition. There is strength in unity and always trouble in a breakup.  And by the way, looking to split any part of India is considered treason and punishable with a jail term.