If I put the wrong blower relay in what damage will that do

I looked at 05 avalanche 1500--automatic hvac. The blower fuse is hot all the time. The fuse has an input leg and output leg, even if the fuse is blown, the input leg would still have voltage. If no voltage, you could use jumper wire connected to voltage on the output side of fuse cavity to see if blower would work. If you use jumper, use an inline fuse.
Yes, it could be something wrong with fuse box or wiring circuit?

normally it is the resistor,( relay) then resistor module then motor.
did you test the relay(I believe located under hood, relay/fuse center), If OK check plugs and wires for melting, damage and good connection, grounds should also be checked. Use a volt ohm meter to see if you are getting any power ti motor,etc.
the first link below gives good how to diagnose blower,press the helpful button
GM Blower Motor Resistor Diagnostics by Wells

DIagnose and Replace GM blower Control Module

http://www.gmcproblems.com/tsbs/Envoy/2003

no --you can put in wrong size,or you can damage a tab on a fuse but straight insert no

Smack it and see if it comes on. If it does then the motor brushes are bad. If it does not come on, check the fuses. If the fuses are ok, check the voltage on the plug to the motor.

Under the dash on the passenger side.

At the moment, I think something wrong with "totally integrated power module", some people call this the bcm. There is no relay or fuse for front blower motor, there is a relay for rear blower. The dark blue wire is voltage from bcm or if you wish totally integrated power module. You could check the wire circuit/dark blue wire. With hvac turned on, check for voltage at the blower module and bcm, you could also check continuity, no voltage on the system.

CHECK SEE IF POWER GOING TO BLOWER MOTOR.IF YES BLOWER MOTOR COULD BE BAD OR HAVE HAVE A POOR GROUND.IF NO POWER GOING TO BLOWER MOTOR FUSE GOOD.YOU COULD HAVE FAULTY HVAC CONTROL MODULE WHICH IS YOUR BLOWER MOTOR CONTROL SWITCH.

Owners manual lists the fuses as :
Engine compartment fuse # 105, 40A
- This is the power to the blower motor relay to drive the blower.

Cab Fuse Panel, Fuse #22, 10A. This is the power to the switch in the HVAC panel.
- This fuse through the switch to operate the relay coil on the blower motor relay.

The other thing to check is the blower motor resistor, to see if there is any damage to it ( usually this is the blower only works on high )
This is behind the glove box

In the Dodge Dakota the blower motor resistor is located under the hood, on the right side firewall.

Dodge Dakota Blower Motor Resistor Location:



Dodge Dakota with a complaint of no blower operation. After unplugging the harness connector and removing the two screws, you could remove and examine the resistor coils for damage. The heat and subsequent rust damage are clearly visible in the picture below.

Either the blower motor is bad,or the blower relay is bad,check the voltage at the blower motor to see if it is getting voltage.If not,check the fan switch ,and then the relay,it is most likely the blower motor.