Start at the wiring connector at the blower motor. Disconnect it and grab a test light.

1st check if Power is going to the blower motor.

Attach the test light's alligator clip onto a good Ground, probe the connector terminal that has the Pink and White wire going to it with the key in the ON position and the blower motor on, speed on High. The test light will light up if the blower motor is getting Power.

2nd check if Ground is going to the blower motor.

Attach the test light's alligator clip onto a Power source, probe the connector terminal that has the Orange and Black wire going to it with the key in the ON position and the blower motor on, speed on High. The test light will light up if the blower motor is getting Ground.

One of these 2 are going to be missing or the blower motor would work.

Here's the circuit description:

Voltage is provided to the blower motor relay coil and switch contacts. When the blower motor relay coil receives a ground from the HVAC module, the relay coil is energized and voltage is delivered from the blower motor relay to the blower motor.

A varying ground resistance for the blower motor speed is provided through the blower motor controls and resistor(s) to the blower motor Ground.

It's wired like this (I highlighted Red for Power and Green for Ground):

Let's say you didn't have power on the Pink and White wire at the blower motor connector.

First and foremost, the 30 amp fuse #2 and the Blower Motor Relay have to be good. They're the low hanging fruit here. If they're good then it's time to test that part of the circuit.

You'll use the test light like you did down at the blower motor connector to test Power and Ground at the blower motor relay sockets.

I know what you're thinking. "Sounds simple enough but when I pull out the blower motor relay how am I supposed to know which blower motor relay sockets are which?"

In your underhood fuse box the setup looks like this:

Now attach the test light's alligator clip to the battery negative post.

Probe blower motor relay socket 87. If Fuse 2 is providing power to socket 87 the test light will light up.

Next, turn the Key to ON.

Probe blower motor relay socket 86. If it's getting Power through the ignition switch the test light will light up.

Next remove the test light's alligator clip from the battery negative post and attach it to the battery Positive post. Key ON, turn the blower motor control on.

Probe blower motor relay socket 85. (that part of the circuit is labeled "Blower Request" in the wiring diagram). The test light will light up if the Climate Control Module is providing a Ground to blower motor relay socket 85 (to energize the relay coil and close the blower motor relay circuit between sockets 87 and 30 and send Power to the blower motor).

If you aren't getting a Ground there then there's still a problem with the HVAC controls or its wiring/connector

If all that checks out good then grab a heavy paperclip or a piece of 12 gauge wire and if you're sure you have power at relay socket 87, jump relay sockets 87 and 30. 

Repeat the test light test at the Pink and White wire terminal down at the blower motor connector. If you still don't have power there then there's an Open in the wiring between the blower motor relay socket 30 and the blower motor connector.

I apologize for this reply being so long-winded but we still haven't discussed if this is a problem on the Ground side of the blower motor connector. The Orange and Black wire.

If you look at the way this is wired you'll see that Position 4 (Hi Speed Blower) is the only position when the blower motor Ground resistor(s) aren't used.

I'm not going to highlight the entire circuit again. You can scroll up if you need that.

Here's what happens when blower hi speed is selected.

And this is why I suggested turning the blower speed to Hi when you tested the Ground at the blower motor connector. It takes the resistor block out of the equation. Electricity is lazy. It will always choose the path of least resistance to Ground. On position 4 (Hi Speed) it gets to choose either going through the resistors or a direct path to Ground.

So if you aren't getting a Ground on Hi Speed at the blower motor connector, it's either a problem in the speed control, or wiring, or Ground point.

The only information I could find about that G200 Ground Point in the wiring diagram is "behind dash panel, right hand side"

Anyway, if you decide to troubleshoot this let us know what you find out

You have to trace the circuit to find why no juice.  Maybe @jack62 could jump in on this one.  It could be something as simple as a missing ground connection.