I know the situations you will face now, But you will definitely get a job if you have hope and keep trying.
Now things you should do are :
1. Prepare for e-litmus & AMCAT & crack it, it will help you two ways :
a) preparation for interviews.
b) If you crack the AMCAT, the institution will provide campus drives & most companies prefer the AMCAT & e-litmus score. They offer you job opportunities depending upon the marks you get in them.
2. Try to find some connections in Genpact - your relations, friends, senior, etc. They will have the referral jobs in Genpact & If you are selected they will get a referral bonus.
3. Prepare your CV with a cover Letter & explain in short about the GAP
It is better if you prior give a short note about your career gap in your cover letter. keep it short & sweet, so that they would get a rough idea about your gap & why. Don't mention that you are suffering from serious illness & other medical reasons, those are not advisable.
One more idea if you have a career gap but you have kept busy your self in any type of freelancing then you may tell the interviewer about the freelancing you were providing & prepare a brief explanation about the work you have done. The interviewer may get a good impression on you about how dedicated you are in your career.
4. Approach some consultancy like ALP, Live connections they conduct some tests like type-writing & verify your certificates & provide you a good reference in reputed companies.
5. In Wipro every Thursday around 9.30am they will conduct some job drives, you can just try there.
Hop this helps you