Hair dryers usually run 1200-1500 watts on high and can cause a breaker or fuse to blow on overloaded circuits quite easily.
This is not what happened in your case and needs to be looked at closely.
My bet is on a dead short in the dryer or cord itself but, it is absolutely necessary to identify the cause of this mishap with certainty. Otherwise you risk having your home burn down.
Good luck with that and hopefully you find the solution is not too demanding on resources and time.
So you're saying it SHOULD have blown a fuse or caused a breaker, but it didn't? What is a dead short?
I will find an electrician to take a look. I guess I should keep the dryer and not throw it away to show him?