Replaced power supply, PC wouldn't output display or spin fans, CPU troubleshooting LED is lit, now neither PSU works.
I was about to post this as a troubleshooting post, but I solved the issue and would like to share.
Most tutorials I watched involved pulling out RAM, GPU, various other components to narrow down what component is causing the problem. In my case, it was a SATA powered fan hub that I forgot to plug in again while installing the new power supply. Because it wasn't detecting that, it wouldn't display out or spin fans. My motherboard also displayed a CPU error on its troubleshooting LEDs. This is very weird but maybe this will be helpful to someone.
Note, if part of your troubleshooting involved removing the RAM, and you managed to boot with a different RAM configuration, you may also need to reset the CMOS to get it to boot with your original RAM configuration again.