My Employer is not releasing me sooner

Hi Guys, I join an IT organization 5 months ago. For some reasons, I didn't like the work environment and with in 4 months I got another offer which was promising to my ambitions. I informed the manager and HR with written resignation email as well as applied resignation on the company provided portal. But the I got to know my mother's unhealthy state and I decided to talk to management and HR for the early release. I am ready to pay the amount in the lieu of the notice as per the clause in the appointment letter, states as, "Either party may terminate the employment providing with a notice period of 90 days or paying the salary in the lieu of the notice." I inform them 15 days before my LWD (declared solely by me) with stating a reason that my mother does not keep well. Within these 15 days I send them reminders on the email, stating my LWD and my unavailability. Initially nobody, no body responds but on my LWD I get and email stating "we are allowing you leaves" once your work is done at home come back and serve the remaining notice period. I clearly state in the email that I would not come back so it would be better if you release me from the duties, do the full and final and handover the respective relieving letter to me. I am still waiting for them to respond and release me. I do not get my salary as per the HR policies but when it comes to me abiding by the policies and buy the notice period they say they do not have resource as my replacement. I do not what should I do in this condition. Please help me out. PS: I was not assigned with any work before I resigned from the organization. I have no dependency in the team.