Noticed there wasn't any air coming from vents. Checked the fuses to the blower inside the car and both 15 amp fuses were blown. Changed them tried turning on the blower and nothing. So purchased and installed new blower as well as relay for the blower. Same thing happens. Blower will not spin and soon there after fuses are blown... Anyone have had something similar happen?

 

You've got a short circuit.
You neglect to mention the year or model but do a search for the FSM. Use your multimeter to trace the circuit thru the wiring harness. Have you tried putting 12v directly on the blower motor?
Where did you purchase the parts?
If not OEM they may be cheap crap?
Was your vehicle ever in a flood?
Telcoman

 

03 coupe manual and parts came from Auto Zone (relay) and Rock Auto (blower). I do have the FSM and the car hasn't been in a flood...never really had any electrical issues.... Today I changed out the controller thinking that may be causing the problem. Went through all controls turned fan on blower never came on (old blower in). No fuses blown this time then I disconnected and plugged in the new blower just hanging there and nothing. No blown fuses this time either, but there is this weird buzz/hum coming from the engine area compartment. Now sure if that is suppose to happen though..

 

Probably a pinched/damaged/worn wire, start at the blower motor and trace it back, the problem is on the load side of the fuse since it only trips when the relay closes and power is sent to the blower.

To rule out the blower, unplug it, turn the fan speed up, see if it trips. If it DOESNT trip then the problem is the blower motor.