What happens if a company ignores my request?

Escalate to the Data Protection Board of India, which is the adjudicating body created under Section 18 of the Act. The Board can inquire into complaints, direct remedial measures and impose monetary penalties. Note that the Act also places duties on Data Principals: complaints must be genuine, and furnishing false particulars or filing frivolous complaints can itself attract a penalty. The remedy is real, but it is meant for genuine grievances.