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I broke off the hose that goes into this box, and the electrical connector completely fell off and the plugin for it broke. I am not sure how important this is to fix currently but I would like to fix it because it supplies my car with Air Conditioning. If anyone knows how I should go about this then that would be great.
I think the hose you mentioned is the evaporator core and depending on where the break is may have to be replaced. That is a pressurized system and you don't want leaks. The other connector appears to be the resistors that control fan speed. That part should still be available at local parts stores.
Your pic looks like a stock photo. Can you post pic of actual damage on your car?