they'd have to be really loose to not make any oil pressure at all. i've blown 5 2jz's, and the oil pumps i've used even though it was blown, it was still running about 0.4bar of oil pressure at idle, and when i ripped apart the oil pump, my clearances were wayyyy out of spec. but i still had oil pressure, so yeah, you'd have to be wayyyyy loose to not make any.
if you missed the o-ring on the oil pan when putting it back together, you'll loose most your oil pressure through there. then there's that metal gasket for the pickup you could be loosing oil from.
i don't know about that oil cooler, maybe it's hooked up backwards? i'd probably try ripping that off and making sure you can build oil pressure. if so, then it's your oil cooler setup. if not, somethings wrong, and you gotta pull the engine