2003 Hyundai Santa Fe won't start

Hello, my 2003 Hyundai Santa Fe w/auto trans. will not start most of the
time. Every now and then it will start with a quick turn of the key, but it almost
never does. I will turn the key to the "on" position and my lights, stereo, etc
will turn on, but when I turn the key to the "start" position nothing will happen,
no cranking, no clicking, nothing. I know for a fact that my starter, battery,
starter relay, and burglar alarm relay are all in good working order. I tested
the ignition cylinder and it seems to be throwing current through the "starter
wire" every time I turn the key to the "start" position so I ruled out the ignition
cylinder. I tried starting in N and shifting from P-N-P again while holding the
key in the "start" position and it still won't start. So I ruled out my neutral
safety switch. If I bypass my starter relay by jumping pins 1 and 2 with the
key in the "on" position the car starts flawlessly every single time. This leads
me to believe that the problem is either in the PCM, the ETACS Module, or
possibly a corroded G07. So my questions are these, could a faulty PCM or
ETACS Module cause this issue without any other symptoms being present?
(if so how can I diagnose this?). Where is the G07 physically located in the
vehicle?(so I can check for corrosion). And is there something I've missed
that could cause this issue? such as another portion of the burglar alarm I'm
not aware of, or a random plug that might have come a bit loose, etc... I
greatly appreciate any and all help with this issue. Thanks in advance.