A500+ doesn't start with A590

[Vanders]

The A500+ starts independently, but when I connect the A590 HDD the A500+ green light doesn't turn on.

Do you mean the power light on the A500+ doesn't turn on? That sounds like the A590 might have short on 5V (the HDD will spin up from 12V)

You sure its an a590? as they dont have switches. GVP HD+ does.

The A590 definitely has a set of 4 DIP switches at the back.

[Vanders]

Yes, power light doesn't turn on. PSU 5V output at fault?

If the power light on the A590 is on then no, that PSU is probably fine.

If not, could a short occur on the A590-side? Capacitor that turns short instead of open?

Possibly, yes. It's going to be a tricky one to diagnose if the A500 doesn't power on at all. You can also try plugging the A590 in with the top cover & shield removed, turn on the power to the A590 & A500, and check to see if any of the chips are getting hot.