Finishing one year Contract. getting offer from another company.

Hello guys can you please help me with the problem am having now because am finishing up my one year with my current employer on the 10,October,2016.

And I have a offer latter from another company and which I should join them on the 30,September this month and my current employer contract with be left only ten days and i submit my resignation letter since on the 1, September this month but I don't hear anything from them

and i go to the office by my self today but they don't want to understand my point and what the hr said is he will see how best he can help me and he said that he is going to call me on Saturday,

please guys can you please help me the good idea and what to do next because I can't afford to lose this opportunity