Hi JMCenterprise
welcome to the Apple (user-to-user) Community.
Re: "New apple studio display did not turn on when plugged into my 2020 MacBook Air".
Check if your MacBook Air is compatibile with the Studio Display:
Eg:
"Studio Display requires a Mac with a Thunderbolt 3 or Thunderbolt 4 port running macOS 12.3 or later",
How to: Identify the ports on your Mac - Apple Support
"Studio Display supports a resolution of 5120 x 2880 on MacBook Air introduced in 2018 or later"
More info: Set up and use Apple Studio Display - Apple Support
and
For MacOS Sonoma
(or please choose your Mac OS version at the top of the article below for accurate info):
Connect Studio Display - Apple Support
________________________________
Re: "Apple support said check cables".
To find the right cable or adapter for your Mac,
check the connector on the end of the cable meant to plug into your computer.
More info: Adapters for the Thunderbolt 4, Thunderbolt 3, or USB-C port on your Mac - Apple Support
_____________________________________
Re: "Nothing but a black studio display".
What to do: If your external display is dark or low resolution - Apple Support
____________________________________
More info. / support / contact options etc.
MacBook Air - Official Apple Support
All the best :-)