I was stuck on this error for a long time. When I removed the last application that I installed from /apps/splunk/etc/apps/ and restarted splunk, it came up fine. I suspect there was an issue with the latest App that I tried to install. Manually removing and restarting seemed to fix it.
I ran into a similar set of errors in my AWS logs. When I tried to connect to the web interface, I would get a response of "500 No appservers running." The root cause turned out to be auditd hogging disk I/O. Not sure if you have the same issue, but you might try disabling the auditd service and see if that does anything.