Ok, so I was dicking around and did this render. I always wondered

low screen resolution
low resolution textures
no anti aliasing
shadeless materials
lightmaps
realtime rendering (cycles is offline render)

get pcsx emulator and iso of game with desired look from rom hustler or emuparadise and run the game with wre frame setting to see- well, the models in wire frame.
also, a lot of psx games used segmented body parts so they didn't have to deal with shape crush corrections when limbs were bent.
but i would forgo that and just stick to simple meshes and textures.

Ya just use 100% self illumination on textures. Same techniques are still used in games nowadays.