I have joined in one MNC. But due to some issues I sent a resignation mail but I didn't get any response from them. At that time I got an offer in another company so I have joined the company without showing that previous employment. Now I am on the payroll of both the companies. Will this lead to any issues..?
Yes, knowingly being paid by a company which you're not performing work for is a problem. Ethically, you're stealing from them. The exact legal situation will depend on your jurisdiction, but almost every jurisdiction is going to frown on that kind of behaviour.
Get on the phone to HR at your "former" employer immediately and explain the situation. Hopefully you have a written record of your resignation mail.