The reason the fuses are there is to protect the unit from stuff like you just experienced. If the fuses do not continue to blow with a different set of interconnects, you have your solution. If something is wrong with the unit, it would blow the fuse everytime you turned it on. Otherwise, it's an external problem. When an interconnect grounds as yours did, it will pop fuses because of the high input surge to the amp and the subsequent peak out.
Amp blowing fuses
I have a BAT VK-200 amp(purchased used 8 mos ago) and a BAT VK-31se(recently purchased new). 2 weeks ago I came home, put on an album-no sound. I pulled the amp and inserted my old b&K ST-140 mono blocks. When I turned them on one was OK but the other had a loud hum through the speakers, I switched interconnects and it went away. I called BAT and talked to Steve and he told me how to check and replace the fuses in the VK-200 amp. I did this and I was up and running in a few minutes. Could it be the bad interconnect that caused the fuses to blow? By the way these are 10 amp fast blow fuses. I just got the VK-31Se new a few weeks. This is my first piece of tubed equipment, is there something that I should be worried about with that unit? I will be calling BAT agian, but I would like to hear some of your thoughts and experiences.