IT/ITeS companies are covered by all labor laws including ID Act, Shops and Commercial Establishments Act, standing orders etc……….
>>> Since company has not issued appointment letter:
--You may claim no notice period/pay was applicable in your case.
--It has violated Delhi Shops and Commercial Establishments Act; Sec:34
However let your lawyer decide whether to quote from the Act or not.
>>> FNF settlement; It is one of the duties of the Inspector appointed under this Act to ensure all dues to employee that has separated are paid.
Sec:37(b) (i)
FNF wages should be paid on last day in office…………………………or within next 3 days or max. by usual pay day.
There are many threads on similar queries that you may find relevant e.g;
https://www.lawyersclubindia.com/forum/Claims-not-settled-by-the-company-after-resignation-98912.asp#.U1oiL0eBmXU