With the symptoms you describe, I'd suspect a leaking capacitor in the firing/charging circuit or a failing FET in the path between the cap and the flash tube. If you know anyone who does electronics work you may get lucky and find that the part can be replaced relatively cheaply provided an off-the-shelf replacement can be found.

Alternate flashes to use as masters include Metz 58 and one of the 430's. I have more Metz than 580 EXii's due to price difference and increased capabilities of the Metz units. My son has a 430 and it works fine as a master for all of my flashes.