file writ petition in HC to claim said land as compensation was not paid and land has not been used for housing for last 34 years 

If for this time no compensation is received and further the property is not utilised your grandmother if alive or her legal heirs can make a writ petition before the high court claiming the land and challenging notification.

Further see all documents notification need to be seen so along with same approach high court advocate he can help you with it.

Dear Client,

IF the physical possession of the land has not been taken or the compensation has not been paid the said proceedings shall be deemed to have lapsed. Option is available to govt, if wan to return land back if not put to use for acquired purpose. 

And as per amended acquisition law, when any land acquired under this Act remains unutilised for a period of five years from the date of taking over the possession, the same shall be returned to the original owner or owners or their legal heirs,

Have you received an order of acquisition from district collector?

I would like to understand the matter in detail and If you wish to talk, I am available to take calls after 14.30hrs daily.

Regards

G.Rajaganapathy
[deleted]

You can visit TN state government site and check your village GO the site is below

http://www.tn.gov.in/go_view/dept/13?page=1

Your land has been acquired under provisions of land acquisition act 

The 

Land Acquisition Act 2013

allows the acquisition process to lapse if government fails to take possession or pay compensation within five years.

1) Under the land acquisition act the acquisition/notice for acquisition lapses after a certain period of time, also there are certain supreme court judgement which say that if compensation is not paid the land has to be restored back to the original owner. 

2)you can file a writ petition in high court .

Citation. .. 

AP HOUSING BOARD

Vs.

MOHAMMAD SADATULLAH & ORS [2007] INSC 400 (13 April 2007)

The Right to Fair Compensation and Transparency in Land Acquisition, Rehabilitation and Resettlement Act, 2013 (also Land Acquisition Act, 2013) and Land acquisition act ,1894 (now repealed)

1. Return of unutilised land.

When any land, acquired under this Act remains unutilised for a period of five years from the date of taking over the possession, the same shall be returned to the original owner or owners or their legal heirs, as the case may be, or to the Land Bank of the appropriate Government by reversion in the manner as may be prescribed by the appropriate Government.

A Division Bench of the Madras High Court on Tuesday reversed an order passed by a single judge of the court in January 2015 directing the State government to reconvey 11.26 acres of unutilised land out of 13.93 acres acquired by Tiruvottiyur Municipality in 1964 for a drinking water supply project.

If the land has been acquired then you can stake a claim on the same for a reason that nothing has been done by the government. 

When was it acquired? 

Regards 

Northern Indian Glass Industries v. Jaswant Singh 2003 1 SCC 335

Supreme Court has held that the High Court was not right in ordering restoration of land to the respondents on the ground that the land acquired was notused for the purpose for which it was acquired.

It was held that after passing of the award and possession taken under Section 16 of the Act the acquired land vests with the Government free from all encumbrances. Even if the land is not used for the purpose for which it is acquired, the landowner does not get any right to ask for restoration of possession.

If the government remains silent without utilizing the  acquired land for the purpose of acquisition made for more than5 years then the land can be returned to the owners.

You can file a writ before high court seeking relief and remedy.

The land acquisition act itself provides the provision for desired relief.

you can try the same filing a writ petition in HC