On GMs now adays the Engine Control Module controls the starter relay. It will look for a park/neutral signal from the range switch and a crank signal from the ignition switch/Body Control Module.

A break down of the starter relay terminals. If you pull the relay you'll see it's labeled on the bottom and has a diagram on the side.

85 - ECM sends power to this terminal to energize the coil.
86 - Grounded to the frame.
30 - Fused, always hot (B+ - Battery Positive).
87 - Goes to the starter solenoid.

Pull the relay, check terminals 30 and 86 for power and ground. Be careful when probing the relay terminals if you can't touch the relay terminal with your multimeter probe don't try to force it in. Use a small pin or attach a male terminal end that properly fits the terminal to a piece of wire.

Start with terminal 30, if you don't have power (12+v) on terminal 30 or if you have less than battery voltage check the starter fuse in the underhood fuse block. Ground your multimeter to the B- (Battery Negative) and probing the exposed terminals. Is there a difference in voltage between either post? If so replace the fuse. Visual inspections don't always reveal issues with fuses. If there is B+ voltage on terminal 30 move to the next terminal.

What about terminal 86? Is it grounded? Check the ground point G109, is it clean and tight?

How about terminal 87? When you probe the terminal it should be grounded since the starter grounds to the engine block. If it's not check the engine block to frame or battery connections. What happens when you jump power to terminal 87? Since you had the starter tested it should spin.

So onto terminal 85, where I suspect the problem is. You stated that there was no communication with the ECM (It's possible it's the scan tool, but unlikely in this case.) and the check engine light didn't come on KOEO.

So, where to start? Check the ECM and ECM IGN fuses in the underhood fuse block the same way you checked the starter fuse. Is there a difference in voltage between the two fuse posts? If yes, replace the fuse. If both fuses are OK, you need to gain access to the ECM. On the 3.6 the ECM is located in the left front of the engine bay.

Off the top of my head I don't remember the type of connector that's used. In general there should be a lever with a tab that needs to be pressed down. This could also be a 7mm bolt that needs to be loosened and the connector will pull out. Or it could be a sliding lock that needs to be pulled.

Once the connector is released from the ECM, there is a plastic cover that protects the back of the connector. There are usually four tabs that hold it in place, this cover needs to be removed. On the front (sometimes on the back) of the connector you should see labels Identifying the first and last terminals of a particular row.

A note on checking ECM connector terminals: Best practice is to slide a backprobing pin along the wire, being careful not to damage the weatherpack seal.

You're looking for connector X1 terminals 19 and 20 (pink and red/white respectively) these should both have B+ voltage. And on connector X3 terminal 73 (black) a ground. Terminals 19 and 20 are the ECM and ECM IGN fuses. If you see less than B+ voltage there is a problem with the wiring from the underhood fuse box to the ECM. Terminal 73 grounds to the engine on the 3.6, G107.

So if everything on the start circuit looks OK and the ECM is getting power and ground. It could be that the ECM is bad and needs to be replaced. Another possibility is that there is a problem with the GMLAN data bus.e.g. one module is bad and shutting down the network.