No Eletrical power till Engine Starts

Hope someone has come across this problem before.
I have a '93 Maxima that has been having wierd eletrical problems all it's life that I have been able to live with or found a way around, but yesterday the ultimate happened, and I'm really stuck.

All of a sudden there is no eletrical power on at all, but the car will start. Once the engine has started, and you blip the accelerator, all power returns, and car runs fine till it is switched off.
When I say no power, I mean, no power. The clock resets it self, the radio lost all its settings, no interior lights, no instruments, no warning lights when key on Aux, cannot even move the shifter as it's locked nothing. Dead.

Start the engine. Still nothing, but engine runs fine.
once you blip the accelerator, walla, like magic, everything come to life, but of course, clock and radio has lost all settings.

Help please.

Is there a fuse or link the allows current from battery when car shut off?

...Is there a fuse or link the allows current from battery when car shut off?

Yes. Check page5 on the link below this txt...

Bingo

Thank you so much Nahkapohjola
The connection right on the positive terminal was corroded, but it looked to be fine until I took it apart after seeing your answer.
Problem solved
Thanks again

Bingo... terminal was corroded, but it looked to be fine ...

Thks for the input: those corro-dead-beasts are masters of disguise :(

Bingo

Thank you so much Nahkapohjola
The connection right on the positive terminal was corroded, but it looked to be fine until I took it apart after seeing your answer.
Problem solved
Thanks again

THANK YOU for posting this problem! I had the same issues and fixed it by cleaning the battery corrosion.