After checking out the website I am really suspicious that the wiring diagram you may be working from may be wrong.
When you get a factory service manual it covers one year with other makes that are identical.
If you look up the OEM service manual it covers the 2004 Grand AM and the Oldsmobile Alero.
http://www.ebay.com/itm/2004-PONTIA...m25b49f4379:m:ma0-OsEUYbWUAH0RZ5t1BBQ&vxp=mtr
As you can see this manual spans two printed copies, the link you provided claims it includes Pontiac Grand Am from 1999 to 2005.
I am thinking they may have merged some of the data. causing you to work from a incorrect wiring diagram.
Some of the content may be relevant and or accurate as far as replacing parts and what not.
Yet there is no way in the world I would trust this manual to provide accurate and complete information to be used for diagnostics.
If I were you, I would sign up for Alldata. and start reading any related TSBs for condition your car has.
If I didn't find anything relevant I would start tracking down the problem with the diagnostic flow chart for engine not cranking.
Then use the provided OEM wiring diagrams for the 2004 Pontiac Grand Am ( referencing ) the connector locations as well to get to the bottom of your problem.
If the suspect connector does not show up on the known good diagrams.
You may be able to track it down by just removing the instrument cluster which should be pretty easy.
Since I am not there, and its your car that will have to be your judgement call.
at least I would try to see if the mystery connection blue tab can be put back together securing the wires in the connector better.
However I am just going by what I viewed in the picture.
Also let us know if the wires are a different gauge and or color from the known OEM wires.