The computer seems to hav 8x4164 and 2x4416 and all of them are 5v DRAMs. So there's no -5v on board.
Looks like 8x 4116 to me... 
Maybe there's a small zener diode or -5V regulator on the main board, or the 4116's are 5V-only types (yes those exist! Mostek MK4516 for example).
IMHO, +5V regulator on this board is not linear, but rather switched-mode.
Yep, maxis could be correct there. A regulator like 7805 would cause excessive losses with ~23V DC input. The way around that would be a separate transformer winding with lower AC voltage, but that doesn't seem to be used here.
So then you'd have a psu similar to the one in a Philips NMS8245, but with a single center-tapped transformer winding, and discrete components for the +5V switch mode circuit. I'll guess a bit more: D3 and D4 used in -12V circuit, D6 a big Schottky diode (one side connected to GND), that coil (next to VR8) connected between a switch transistor and +5V output, smaller coil (L2) maybe for some additional filtering on that +5V line. 7812, 7912 and a big PNP transistor or P-channel FET on that cooling block.
Please post silkscreen (pcb) markings for those parts on the cooling block as well, agnul75?
IMHO, +5V regulator on this board is not linear, but rather switched-mode.
Yep, maxis could be correct there. A regulator like 7805 would cause excessive losses with ~23V DC input. The way around that would be a separate transformer winding with lower AC voltage, but that doesn't seem to be used here.
This is what I thought. 23->5 Volts with a 1.5A current is a bit something -> 30 Watts to dissipate. The computer will melt down.
So, the big inductor L1 is a primary inductor of a chopper (connected to the power transistor), and the small inductor and two capacitors form the PI filter.
Here I give a couple of examples of a similar 4-5 transistor regulators which I used long long time ago...
The one below I was using on my very first knock off back in 80s.
Here are a few examples with a similar classic topology. Also, two out of 4 of small signal transistors in Fenner's power supply can be organized in the differential pair to make an error amplifier (since there is no TL431 or any op-amp on the main board).
Hope this will help.
I'm a stubborn and i have tested the computer with another power supply and it works !
After i have read all post and the winner is tvalenca.
In the cartridge slot is missing the inhibitor switch !
I have closed the CN6 connector on the board and computer working with the original power supply.
Now i replace the inhibitor switch on the cartridge slot.
The plastic part are now in my washing maschine for deep cleaning.
"another msx saved from oblivion"
Thanks to ALL
First of all, kudos on saving it. I am glad that I helped.
the inhibit mechanism is part of the standard, and on earlier designs makers were more concerned on following the standard, I just connected the dots. 
I also made this mistake on past, so...
anyway, the layout of this PSU is rather odd. I think our folks Maxis, Alexey and Retrotechie would be interested on more detailed pics from its board.
Congratz! That was an easy fix luckily.
I have closed the CN6 connector on the board and computer working with the original power supply.
Great! Nevertheless consider checking and if necessary adjusting the +5V voltage with VR resistor.
I think our folks Maxis, Alexey and Retrotechie would be interested on more detailed pics from its board.
I'm very interested indeed. Simply never seen anything like that in western computers
It works
