Welcome to genvibe!
I attached a copy of the 2004 Matrix heater wiring diagram, which should be the same for your 05 Vibe
The blower motor gets 12V from the HEATER fuse which then goes through the HEATER relay. That relay is activated by the GAUGE fuse. If the GAUGE fuse was blown, you'd have more problems than just the blower. The GAUGE fuse gets power when the ignition switch in in the ON/Run position and it enables multiple other independent circuits
You said you checked the HEATER relay. It's above the glove box, there's four relays, the heater relay is the one that's bigger. Some people have had the TAIL relay in that relay block work loose and lose their tail lights, might happen for the heater relay as well I suppose. (There are pics in viewtopic.php?t=5078
) You could probably reach up and over that relay block to make sure they are all fully seated without having to unscrew the block from the dash frame. The fan relays in the under hood fuse block are for the engine cooling fan, not the HVAC blower.
The HEATER fuse is one of the three giant fuses in the awful to access under dash fuse block (the one closest to the micro fuses)
The blower motor gets ground from the Fan speed switch. When the speed is set to HIGH, it bypasses the blower resistor and puts no resistance in the motor circuit, so the fan runs at max speed. When the speed is set to second highest, the ground routes through a piece of the blower resistor, and at the next lowest speed it runs through more of the resistor. The more resistor, the slower the motor. When a resistor goes bad, the fan should still run at the highest/max speed
I'd probably disconnect the wire from the blower motor. Turn the fan speed to the highest setting. Then turn the key to ON/Run (engine doesn't need to be started) and check for 12V on one of the pins (The diagram says it would be the solid black wire, but you could check both) Then turn the key off and check for continuity to ground, (which the diagrams says it should show up on the black w/white stripe wire) The one that was 12V should be open circuit, the one that wasn't 12V should be ground. If its working right,these two tests would get you 12V on one, ground on the other, and if you do then the blower motor is suspect.
If you don't get 12V, then it's either the HEATER relay or the HEATER fuse, or it could be the speed control switch not sending ground to activate the HEATER relay.
If you don't get ground at the blower when the speed switch is set to highest, then the fan speed switch is suspect.
Or it could be some wire damage somewhere