Hi,
As there could be a number of reasons for your problem unfortunately there is no simple answer.
It could be anywhere from a loose connection to a problem with a protection circuit etc.
The best way is to follow the No Power troubleshooting flowchart in the service manual to diagnose the problem.
Here is a link to the service manual for your receiver. Scroll to Sect.5.1 (p.28) to view the procedure.
https://elektrotanya.com/pioneer_vsx-521...
To download the file, when the sentence below the Document Preview box changes from This file is downloadable free of charge: ...processing... to This file is downloadable free of charge: Get Manual, click on the Get Manual as this is the download link. Be patient as it takes a little while to find the file. (See images to see what I mean)
(Click on images to enlarge for better viewing).
Hopefully this is of some help.