Chosen Solution

It feels like… loose. Like the console does not grab very well the cartridge. For that reason most of my games dont work (blinking screen).

You can disassemble the NES and replace the existing cart loader with a female-female 72pin connector. You’ll probably be able to find one on the net with a little searching. Otherwise you can use a jewelers screwdriver to bend the old contacts down a bit. This is a well known issue. There is a lot of information on the net.

There are parts available on ebay to fix this. Called a nes cartridge connector.

Be careful of some replacement cart connectors as they can actually be too tight and damage the cartridge edge connector (PC-board). Try cleaning the cart connector with alcohol first or bending the pins slightly with a screwdriver. I did this with mine and the original connector is now operating much more reliably. I hope to avoid replacing the part as long as possible.

You should probably look online for a replacement 72-pin connecter. If something is loose or broken it could make the cartridge fit on looser (perhaps from loss of pins.)