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well first we need to know what year blazer and the engine and milage but here are a few suggestions to check

1) is your antifreeze leaking out or just dissapearing? The blazers are notrious for intake manifolds leaking or a headgasket could cause this loss also. Id pressure test the coolant system and the do a compression test .

2) How did you check the wiring? It seems like it would have to be in the wiring somewhere for both of these to go out. i was thinkin maybe the switch but if the third one is lightuing up then it shouldnt be that. recheck your wiring

3)what were you doing when tranny slipped cause I have heard alot of things about the actautor valve in the tranny pan making it seem like its slipping but wed need to know more to really help and check your fluid it might just need a change