It seems as though there may be a lens problem, which unfortunately, is fairly common with a lot of cameras.
The problems usually are caused by:
Sand or grit interfering with the lens extension mechanism.
The camera has been dropped with the lens extended.
The camera has been powered on, but the lens had been blocked preventing its extension.
The camera was packed in too tight, compressing the lens.
It can even happen with regular use where nothing was done wrong.
Try the following:
Blow compressed air in the gaps around the lens barrels to hopefully blow out any sand or grit that may be in there jamming the lens mechanism.
If you do notice anything around the barrels and it won't dislodge using compressed air (or even a vacuum cleaner) try "gently" tapping around the lens barrels with a pen etc., to try to dislodge any particles that may be jamming the lens barrel mechanism. At the same time turn the camera on and off as you're doing this.
There are a few more extreme methods but they could potentially cause more damage to the camera lens mechanism and still not fix it.
You could try replacing the lens mechanism, (here is a link to the ifixit Canon PowerShot SX520 HS Lens Replacement guide) however searching online indicates that you can get a good used working SX520 HS for less than the cost of the replacement part.
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