Does it not power on at all? Or does it try, and turn back off when it fails to initialize the lens?
You can buy a new lens assembly from Ebay.
https://www.ebay.com/itm/Original-Canon-PowerShot-SX530-HS-Lens-Zoom-Assembly-CCD-Image-Sensor-Board/182872485617?hash=item2a940caef1:g:KhcAAOSw-5dZ-y5x
Follow the teardown guide to replace the lens.
[[Topic:Canon PowerShot SX530 HS]]