Powerless dead zone when accelerating, cold.
 

Hey guys,
I’m new to this forum but a long time Yota lover, and committed father to a old 4runner.
I bought this 1994 runner about a month ago, and the guy had replaced timing belt, mass air flow, cap, rotor, wires, plugs, radiator, water pump, therm., and much more. Motor has good compression, spark. When cold is has NO power, and starts jumping/bucking while accelerating BAD. Throws check engine light only after running for 45 minutes or so. Not getting hot at all. Also, while accelerating it generally has very little power (even for a 3.0, as I’ve owned 6 and this is the slowest) but what’s weird is it has even less power between around 2700-4000 rpm. It’s like a dead zone. I cannot figure it out. Any help be much appreciated. Thanks!

Check the intake tube very closely, even remove it and really check the bottom for cracks that will bypass air around the maf.
What is the code for the engine? O2 sensor could also make it run like crap, or tps will change timing so it won't advance on accel.
Check tps idle position also.

So I checked the TPS with multimeter and it is showing readings in spec. I don’t know how to check the code though, it’s OBD1.

When you check the tps, did you check the idle contact also?
Check ignition timing at idle and just off idle, it should jump advanced about 20 degrees. If the timing doesn't jump up just off idle, then the tps needs to be adjusted.
The engine code can be checked by shorting the TE1 and E1 contacts in the diag box under the hood.
The check light will then blink the code out, they will be 2 digit code with a 1.5 sec pause between the code digits, 2.5 sec pause between codes (if you have multiple) and 4.5 sec when it restarts back to the first code.