It is but natural that you will face some problem without having experience letter as well as reliving letter from last Company. It is your experience certificate which will prove your work experience and apart from this it will be better for negotiation with offer provided by the new company. You have to approach your previous employer, if you have left your service for providing experience as well as relieving letter if you have left your job.
It seems from your query that your name was not upon the muster roll of the previous company, that's why they were paying your salary in Cash, in present scenario everyone have big concern for financial transactions regarding payment of salary to the employees, obviously your company will also be audited by the Auditors from time to time. Kindly make a gentle request to your employer to provide the same.