My Galaxy (admittedly a TDI) has the same fuse layout as per the picture- 2 green 30 amps in the top two positions and a purple 3 amp at the bottom. The 30 amp fuses (listed as 2/3A in my owner's handbook) are to do with the ABS as Chris says in his reference library article. The handbook is a bit unclear as it doesn't show a diagram showing the fuse location in relation to the fuse numbers it gives, but if fuse 1A is the green (which should actually be purple!) fuse you are removing for the 'power supply on board electronics', this could be a power supply to the various modules e.g engine management.
If this is the case and the fault resets by removing and refitting this fuse, I'm thinking it may be a relay 30 issue- a dodgy relay which 'resets' by cutting and reinstating the power supply to it. Relay 30 is a common fault (it supplies power to the engine management) on the 2.3 petrols which affects engine starting and running.
It does look as though the fuses/ratings you have in that battery fusebox may also be incorrect, but I doubt that is the cause of your problem.
I stand to be corrected as I don't have any more in depth wiring or fuse info but relay 30 could be worth a look/substitution.
