How to search for broken Splunk forwarders or Indexers without using a .conf file
What do you mean? Please expand upon the use case. Explain "broken" and "without using a .conf file".
Pretty much everything in Splunk uses a .conf file in one way or another so it'll be interesting to hear why you don't want to use one.
The Monitoring Console has alerts for missing forwarders and indexers, if that's what you're looking for.