This most likely points to an internal fault in the flash, not the camera hot shoe.

A shoe-mounted flash should be able to power up and charge with fresh batteries even when it is not on the camera. Once charged, the ready/lightning-bolt indicator should come on, and the flash should fire from its own test/flash button independently of camera settings.

Because your ON light does come on, the flash is at least getting some power. Cleaning the battery contacts is still worth doing, since corrosion can reduce current flow, but if the flash never reaches ready status or fires its own test button, the issue is probably internal rather than a hot-shoe connection problem.

Use fresh batteries, clean the contacts, then test the flash off-camera with its test button. If it still does not charge or fire, it is likely defective. Avoid opening or servicing it yourself unless you are qualified, because flash capacitors can store dangerous voltage.