I would like to know what is the most reliable way of checking system health status remotely. For example I know you could ping a server and if you get response then you could assume that server is fine but this might not be the case all the time.
Being able to log into it through RDP, wmic\wbemtest or a VNC client are usually pretty good indications that it is up and running. Just remember that the Remote Registry service is turned off by default these days and there maybe a few more considerations depending on the purpose of the system and how it was set up.
If you get a valid handle back then great, that tells you that the system is up and you can close that handle. If not then the resulting error code will tell you what the problem is.