I can start the web sphere server normally at the start of the computer. If I want to restart or publish the server, it works perfectly fine. However, once I stopped the server, I could not start it again no matter how I try. I have to restart the computer to make it working again. The error message says that
Starting websphere application server classic v8.5 at localhost has encountered a problem. Cannot connect to the server process. Make sure the server is already started.
Any idea on why this is happening and how to solve that
When stopping the server you should try to use the stopServer(node/manager/etc).sh
Now as it was mentioned before in the comments, if you are seeing that error it means that there are still some other WebSphere process running. Check the process by going into the Task Manager -> Processes (Check the Box for "Show processes for all users").
Usually the WAS process are named java and WASService.exe. The java process for dmgr is usually 200,000K or more, Node Agent and Servers might be smaller depending on your env. The WASService.exe is much smaller than the java.exe one. Now you could kill these processes and that should help. In addition to that you can go to the Services section of the task manager and you can review the ones known as IBMWASXXServices and these can also be stopped (I think someone else suggested this as well).
Finally if you keep struggling with this issue, it might be good to open a PMR with IBM and you will be helped to solve the issue.