Unfortunately no check engine light.
So did you actually check for codes, or just noting that the check engine light isn't on?
I'm not quite sure what you mean when you say it "acts like it wants to run then just dies", when you try to start it, does it fire then die, or does it just pop once or twice?
Try this if it actually fires for a second then dies. Hold throttle all the way to the floor and start it. Will it actually run normally?
FYI, depressing the throttle to the floor will put the ecu in open loop via tps, and it won't process any data from the flapper door (as well as o2 sensor and probably the iac too, not sure of that one though) is on the afm, this may tell you if its a massive air leak and/or afm issue before the afm that's causing it or not. It will also tell you whether the engine actually runs or not, which should rule out timing.
Also, not sure how you're adding fuel to get it to run, are you dumping it into the afm? That's not a very good thing to do if you are.
Hopefully you don't have the intake tube off the throttle body, it HAS to be connected directly to the afm for the engine to run. There cannot be any openings whatsoever between afm and tb, as that's how the afm measures air flow into the engine.
At this point, I'd just go through all the steps from a to z. Check plugs and see what they tell you. It will also tell you whether you're getting fuel or not. Assuming you've cranked on this engine for quite a bit of time, the plugs will most likely be a bit wet if fuel is flowing properly. This will also be a good time to replace them with new plugs. Next, change teh pcv valve, its just good to have a new one in there anyways.
Since you've already replaced the cap and rotor, skip that step. Next should be physically checking all the wires, make sure nothing was knocked off the engine or shorted out from the accident. I'd start from the battery, grab the first wire you see and quickly check to make sure the other side is plugged into something or running into the cab. There's a lot of wires and peripherals on these engines, its gonna take a little while.
Next would be to check every vacuum hose on the engine. You'll need to make sure nothing is missing a hose or disconnected.
After that, get a multimeter out and check the tps on the throttle body. Follow the manual for the check, and once you know its working properly with the 2 flat gauges inserted at the throttle stop screw as shown in the manual, short your check connector and see if any codes are stored in the ecu. You cannot check for codes if the tps is off, and unless you can confirm you're just getting the quick even flashes, you'll need to set the tps properly for it to work.
Once you've confirmed you have no codes, check the afm again, this time with a multimeter and run through the manual's check directions.
As for the IAC, that should not keep the engine from starting, its job is to kick up/down the throttle, not keep it from running, even if its broken.
Once you go through all of those steps, I'm pretty sure you'll find the issue and once that's fixed, you'll have a 4 runner to drive.