OK, so a couple of recommendations. If you are worried about compatibility, you can go to
https://pcpartpicker.com/
and "build" your computer and it is pretty good about letting you know about compatibility issues at the bottom of the page. Without knowing your entire build no one can know if your 450W power supply in enough to power your system.
I am going to ask some questions and they are not meant to be demeaning.
Have you re-checked all of your connections and re-seated all of your components and power connections?
Does your CPU Have an iGPU? If so you can use the MOBO video out to the monitor and see if you can get it to display.
Looking at the card it appears to have two power connectors on the pcb. A 6 and an 8 pin. Do you have both plugged in from the PCI power cables?
Depending on the fan curve for your RX580, the fans may not start spinning until the card warms up to a certain temperature. My 5700XT fans do not spin until I start gaming, I don't think this is an issue.
If you can post your build and let us know what you have done, I am sure more folks will start to help.