Toyota Repair: 94 Supra Erratic Starting, automotive electrical systems, fuse box

Question
We have a 94 Toyota Supra, non turbo, 6 cylinder, standard trans, 75000 miles. Last few weeks we have an inconsistant starting problem. Will turn the key over and get nothing, sometimes several times, then boom, it starts. The first few times there is no power at all, no radio or idiot lights, no starter clicking noise, just nothing. Then suddenly you turn it over and it's a perfect start. Once it starts it is generally fine, although on two or three occasions the car, while sitting at a stop, will low idle then die out unless the gas is pressed to rev it up. This only occurs shortly after having been started. Toyota really has no clue other than the main fuse box may have some connection corrosion. No pattern to when it does or doesn't start. Our regular mechanic looked at the ignition wiring and noticed corrosion, which he cleaned. No change however. Any suggestions you have would be greatly appreciated. These cars are so rare and we really don't want to sell it.

Answer
The fact that there are no dash lights and there is a no start condition means that there is a total loss of battery power to the system so make sure that the ground connections from the battery to the body are good, they also used to have fusible wires attached directly to the positive battery terminal which feed all of the circuits of the electrical system, these can become corroded inside the insulation or break, there is a loss of power or ground between the battery and the rest of the car, that's obvious, you need to find someone that knows automotive electrical systems to find that problem.