I had the same problem. I ran "splunk stop" and it killed the processes I could see in Task Manager. When I ran "splunk start" I noted that the http port was running on 8001 not 8000 as I expected. Hope this helps.
,I had the same issue. When I looked in Task Manager there were 2 processes running. I tried "splunk status" and it popped a second command window which disappeared before I could be sure that anything was running.
I ran "splunk stop" which killed the processes mentioned before and then ran "splunk start". The second window again sporned after the Window privilege warning. The startup ran fine but I noted that the http port was 8001 not 8000 as the doco indicates. Changed the port and it might work!
While there are likely other ways to do this, I would open an elevated command prompt and issue the start Splunk command. This will provide feedback to ensure the Splunk service is actually started, as well as giving you the URL that the Splunk service is listening on (to include https:// if you've enabled that).
Get your command prompt to the C:\Program Files\Splunk\bin directory and then type splunk start