We had our 06 Sequoia shipped to us. The shippers took it from the ship at port and drove it to the storage unit on the Navy base here for us to come pick up. (side note:No problems with the car. Less than 20k on it, car has been babied). They stated that it was completely fine when it arrived. We go in to pick it up yesterday and they come to tell us it has no power, they think the battery needs a jump. They attempt to jump a v-8 4 times with a partially powered up "zapper", said it would start up but they would give it gas and then it would die. They also tried to jump it with a golf cart we were told.
We go back there, take the battery out, get a new one and put gas in even though there was some already in the tank. It turns on fine with the new batt but we notice that NONE of the electrical items work. ..IE no radio, no lights, no power to windows or door locks or seats etc..Within a minute or less, the vehicle dies again! So we check fuses, 12 were blown and there were black marks all around the fuse housings. Still, after replacing all of them, the vehicle will start, stay cranked for about 30 seconds then sounds like the timing is off or something, chugs a little and dies.
What is going on here?! Any ideas?

It sounds like the whole wiring system in the car has been blown. Judging by the black marks all around the fuses there was probably a HUGE surge of power that blew out all of the components or wiring before the fuses could stop it. Its like running 100 volts through speaker wire, it will just burn out the wire. Someone may have tried jumping it from something way too powerful, such as a wall outlet, and that would fry it.

As for the engine your alternator may be malfunctioning too and ignition may be off. Ignition could definitely throw off the timing in the engine if the spark plugs are not firing right.

In conclusion: someone has done something to that car that they werent meant to. It will likely be very costly to get all that replaced, the wiring in the car is all tucked away and if that requires replacing it is a huge job.

My advice would be to get in contact with the seller because you do have some buyer rights and if it has a bunch of problems they didnt tell you about you can sue in small claims court

Sounds like the catalytic converter may be screwed! If the contents come loose and stop up the exhaust the car will start, run about 30 seconds and die. The electrical may be a different issue.