I just got my 1993 LS400 1UZ fired up a few days ago. Too bad I left my books in the car, 2500 miles away from me, but I can try to help you diagnose what is happening.
First off, try reading if the ECU stored any codes for you. The diagnostic connector on the motor should work if the ECU was wired in correctly. Jump pins TE1 and E1, then the "Check Engine" light should flash out the codes. If it just stays flashing steady, it has not stored a code since power was connected. Makes sure you have constant power to the batt lead of the ECU and try cranking it over. If it is missing any sensor leads, it should set the codes pretty fast. I had the Fuel Pump ECU from my donor car, and it is running my Bosch fuel pump just fine. Without the FPECU, it will store a code, but it should run fine with the pump wired to run with ignition on. You can also try a compression check. If you are getting over 140 psi in each cylinder, then you know the cam timing has to be pretty close. When I finished the wiring, I also went through and just checked virtually every pin of the ECU to make sure it had the correct signal, power, ground, or watever the book called for. I left all of the ABS TRAC and CRUISE wires open, and it has not set any error codes. My tank was 1/4 full of 4 year old gas and it still fired up quick. I did die after a few seconds the first time, but that was due to a few vacuum leaks. The brake booster hose lets in enough un-metered air that it goes very lean. For it to fire in cold start mode, it only needs the AFM signal, NE, G1, G2, Igniters, Injectors, TPS, and Idle switch. It pretty much ignores the rest of the sensors until it starts to heat up.
Good luck getting it running. I was so pleased, and relieved when mine fired to life. I still had open headers, and the roar was shocking.
Gary M.