I tried sending you a reply to your question, but Yahoo returned it. Here it is:
With respect to the Icom IC-706, the negative lead is connected internally to the case of the radio through several circuit board traces, and three clip-on heat sinks which contact the outer case.
Remember, there are two negative, and two positive connections on the battery. This subject is covered in my Wiring and Alternator article on my web site.
Here is the scenario as best as I can explain it with out a schematic: The BIG negative lead from the battery goes to the engine block, close to the starter motor. The BIG positive goes to the starter relay/solenoid. When you start the engine there is a voltage drop across these leads. In cold weather, it is not uncommon for the voltage drop to be 2 or 3 volts. Remember, the inrush to the starter motor can be as high as 800 amps, and in some cases (shunt style starter motors), 1,200 amps!
When you connect the negative lead of your radio to the engine block, it had the potential of what ever the voltage is at that point on the engine block where it is attached. The frame of the radio is at a different potential. How much difference depends on resistance of the conductors, both in an out of the radio, the chassis resistance, the SMALL (accessory) negative lead (battery), and even the resistance of the fuse.
When you start the engine, the effect is to express a voltage across the negative lead of you radio's power wiring. As a result, the fuse in this negative lead had 2 or 3 volts expressed up on it. Since the resistance in this lead is about .2 ohms give or take, enough current flows through the lead to blow the fuse.
The radio still operates, because it is getting is negative return through the various chassis connections. Which, incidentally, isn't a wise thing to have happen! If you were to transmit in this fashion, there is a possibility to burn those aforementioned traces, and/or the heat sinks.
There are two schools of though on connecting the leads directly to the battery, or to the chassis point when the accessory ground attaches. The reason is, amateur radios chassises are NOT isolated, but commercial radios chassises are.
What I'm puzzled over is, why did you use a 10 amp fuse in the negative lead?