Here is a summary of the situation so far. My car starts up fine and runs on 4 cylinders briefly before going into idle mode where cylinder 3 cuts out. I think the engine also goes into some kind of limp mode because the engine won't rev above above 1100 rpm after cylinder 3 cuts out. The DME is throwing two codes:

P1106 Manifold Air Pressure Sensor Too Low at Engine Stop(I've cleared it and this one is thrown with Key On Engine Off)
P1688 Electronic Throttle Control Monitor Level 2/3 Air Mass Flow Calculation(this one comes on after the engine is started)

As far as trouble shooting goes I have taken these steps:

-Ohmed out the Coil Pack. Readings are normal so the coil pack is ok
-Switched spark plugs and plug wires between cylinders 3 and 4. Same condition resulted meaning the spark plug and plug wires are ok.
-Cleaned the injectors. Same condition resulted
-Switched injector 3 with injector 4. Same condition resulted meaning the injector 3 is ok.
Reset the DME multiple times. Same condition was still there.

I got a replacement DME and had it realigned to my car. So I'm thinking right now it might be a bad replacement DME. I haven't tested the MAP sensor properly yet. Freeze Frame data showed the MAP was at 11.2 in Hg at 0 rpm and 7.2ish in Hg at 1400 rpm. I don't know if that value is actually in PSI because my baro press. should be 11.4 Psi at my elevation. I also unplugged the MAP sensor and it didn't affect the condition. I think it's the replacement DME unless someone can tell me something otherwise.