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All the REST commands related to Virtual Machines can be found here.
The instance view Command will get you the status of the VM to see if it is running or deallocated.
If you attempt to start a virtual machine that is already in the running state, the command will simply error out stating the VM is already running. It will not impact the VM negatively in any way. Here is the API command to start a VM.
An example in PowerShell after running the start command is that you get a response back stating that the VM is up and running that the command was successful. The same is true for a REST call. And as mentioned above, you can always use the instance view call to get the current power status of a VM.