Installed DMA in my local machine (Latest Windows Server) and it's up and running in the background too (as second below image shows). But I can't be able to connect either from the browser or cube. Showing that Dataminer is not running.
There are a lot of processes down including SLElement, SLAutomation. This already indicates that your local DataMiner agent is not running correctly. There is a lack of information here to properly answer your question as there could be many answers possible. You can try a restart of the DataMiner agent but I cannot guarantee you being able to connect to the DMA afterward as there could be some issue preventing the DMA from working correctly and therefore a restart can be not enough.
You can check DataMiner logs to troubleshoot where you have the problem. Maybe SLDataMiner, SLDMS or SLConnectivity give you more information about the problem. As you can't connect via Cube, you would need to check logs on the server folders C:\Skyline DataMiner\logging.