Oo thats quite a biggun then?
As you're from Norway, I suspected the mains voltage would be 230V, so I'm sure you realised that for a 1A fuse to blow on the primary, it must have been carrying >230W. That said, if I erroneously assume that its 50% efficient (its much more, just for arguments sake) then thats 115W in your primary. If that was across a single diode, via the grounding connection in your scope, its arround 11.5A flowing....
Anyways, I coudl go on about howmuch current flowed where. As for the original question:
1. Check the diode rectifier with your multimeters diode check. Fried diodes = a voltage drop of < 0.5V (most are 0.6-0.7, but at super low currents can be less). Chances are, even if it didn't get that hot, something in the bridge shorted.
2. As suggested, check the resistance of the windings of your transformer.
3. If you're fairly confident everything looks ok. Plug your transformer into mains, with a 1A fuse, with the secondary(s) open. Nothing connected at all. Any kind of heat, hissing, or other sounds, and dump the transformer.
4. New setup, this time with a common ground