If the screen turns on and looks like it's working but there is no heat, then the problem is the thermal fuse. It takes reassembly and a $5 replacement fuse. I replaced mine with one of the same specifications and it lasted a month. I replaced it again with one that trips at a 10 degrees higher setting and it's been good for a couple of years now.

I fixed 2 of these Breville smart ovens by replacing the thermal fuse. As yourself, they were dead yet the power outlet was good. This is a common fault wit stuff that heats up, like toasters, coffee brewers and such. I got my thermal fuses on ebay and radio shack. Just make sure you take note of the polarity of the thermal fuse before clipping off( they are soldered on) to make sure you place the new thermal fuse just as the old one.