if you're hearing the relay, either the power feed to the window grid is DOA ( possibly blown fuse or broken wire at grid ) or the relay itself won't carry the load, have you replaced the relay or is there on similar close by you can swap ? ( pay attention which one you swap, don't cause yourself more issues )
many defroster grids have a timer ( or even a thermal magnetic switch ) that shut the defrost grid off after X amount of time, this could be part of the switch, it could be somewhere else.