Playing the odds game I doubt someone would configure that station in particular to not output any video signal.
To your original question it's no different than any other embedded, terminal, or PC platform would require. You need a null-modem cable and a 9-pin Standard IBM style serial port to attempt to look at the terminal on this particular station. Most USB serial adapters would probably work on the PC or Mac side if you're going to use a full computer to try to view the serial output.
However in real life the odds are much better that you're using an incompatible monitor. Even if somebody reconfigured the operating system with a totally messed up screen resolution you should've seen the firmware interface come up momentarily with a few basic colors and readable text. Since you saw nothing you're most likely using incompatible monitor or incompatible adapter for your monitor.
All SGI's, including the O2, the only SGI that has a VGA connector, require a sync on green (SOG) compatible monitor to operate and usually has a default output of 1280 x 1024.
Most of use very old 15 to 20 inch LCD monitors from about 2005 to about 2009 or so because most of those supported SOG. I have quite a number of Dell monitors but Samsung sync master, Sony, BenQ, NEC and a few others also supported sync on green right out of the box as stated in their product manual specification appendix.
If you have a green LED and a chime, as you indicated, I would assume you have an incompatible monitor first.
Two things you need to be made aware of as a new owner so you don't run into problems is 1. Do not ever pull the motherboard before you pull the power supply out. Obviously you need to remove the power cable from the power supply before removing anything but always remove the power supply first and put it back last. This insures you will not damage the electronics which can be damaged by removing the power supply out of order. PSU should first out, last in.
2. UNIX SGI stations use a real time clock chip with an embedded battery and oscillator in an epoxy blob that not only goes bad overtime, though you would see the complaint if it did, but also makes it so they can't reasonably be reset to default settings using some magic jumper or button on the device. You have to get in the firmware interface and have a running OS to have a basic chance of resetting to default values. You can also change a bunch of these values by hand if you can get into the firmware interface. This presents a chicken or the egg problem, if someone's done a very odd configuration to the system there's no button on the motherboard or something you can press to reload defaults.
In this case you have two options. You can buy a third-party RTC module that has an external battery which would allow you to remove the battery when the system is off thereby blanking its settings causing it to rewrite defaults and boot up in standard mode the next time it was powered on or a fresh battery inserted. (Make sure you select "fully assembled on product page:
https://www.tindie.com/products/glitchwr...placement/).
The second option is to do what you're planning. Get yourself a genuine null modem crossover cable, get to the firmware interface via the serial port and attempt to wrestle settings back under your control.
Just so you're aware if there is a password on the firmware that actually does have a bypassing jumper on the motherboard to go right through. But unfortunately as I've said, there's no jumper to reset defaults for you.
Before you go spending any real money give us information on how you've hooked up the monitor and what your exact monitor brand and model is. That way we can establish if you should be seeing anything or not. If you happen to have a much older monitor you should try it. Failing that, you can often pick up very old LCDs from the early 2000s that should work with these stations for under a few bucks at recyclers or similar.
Best of luck and let us know how you find things. There's a lot of great resources here to help you out. Go slow and don't force anything and please keep in mind the power supply warning I gave you above.