Absconding after 1 month resignation due to rejection of early reliving

Dear Team, I worked for a company for 1 year and Resigned from the company clearly mentioning the comment to relive me early. I have submitted my resignation on 23-Dec-2021 by requesting an early reliving by 15-Jan-2022 as the hiring company offered me to join before 17-Jan-2022. I have requested my manager, head HR and Site Head to relive me from duties as per requested date. But my request was not considered and I had no option other than absconding to pursue my career in IT industry, the only opportunity I got after a long struggle. Accordingly, I have kept all the company assets in a bag containing Laptop, Accessories, Data Dongle, etc,. in our department office in presence of my other colleagues and left the organisation. As per conditions mentioned in offer letter, I was ready to pay the notice period buy out and other payables that need to be paid. I still stick to the conditions of the organisation. But the HR team of organisation is not responding to mails or calls. I have offer with a big company and they require previous experience letter otherwise my employment is at risk. Please suggest me what I can do to get my service letter.