How do I tell if mac Mini is turned on?

I have a new mac mini. I had it set up fine last week, but there were some issues with adapters etc, so I've had it off all week and been using the old laptop. Now when I try to hook it up using (I'm pretty sure) the same setup, I'm not getting a connection to the monitor. I'm not convinced that the mac mini is turning on- is something supposed to happen when I press the power button, eg, should there be a light that comes on somewhere? Without some indication that it's on, I can't tell if the issue is with the connections/cable or the mac mini itself. (The external monitor is working fine with the laptop, so I know that's not the issue.) Thanks!