Have you done a compression test yet? A compression test will tell you if you have any mechanical problems (valves, timing belt, piston...) When you pull the plugs, lay them in order and note if there is any differents in them. Color, damage... This could also give you a clue what’s wrong.
Assuming your compression is right and you said you have proper fuel pressure check your ignition system. Maybe you have a weak coil. Just enough spark to run the engine without a load.
Last note: I had a EGR valve go bad and it had no power, idled bad and so on... Also usually if your computer goes bad it won't run at all. It's a good or bad type of thing.