When do you need to desolder a rectifier to check if its bad?
If you use the diode test function on your meter and they measure zero in both directions, at least one is probably shorted. To be sure lift one leg or cut a trace and test just the rectifier. 

If you look at the schematic you may be able to see some sneak paths that would be present if a diode is shorted.. such as through a transformer secondary (which is very low resistance). Or maybe something else is FUBAR. Without a schematic it's just guessing.