Alright so this one might be a bit different from the usual test gear and typical consumer products.
So I have a Star digital Ski waxing iron used for waxing nordic and downhill skis (nordic in my case). These are some of the best irons on the market and hold temperature very nicely. The other day I went to use mine and plugged it in only to have nothing happen. I was pretty sad

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I have made a repair to this iron in the past when the rotary dial broke. That was quite a simple job and after ordering the part I was back up and running shortly.
This time the Iron displays no sign of life when plugged in and I am not quite sure where to start.
I've attached some photos of the different components in the iron.
There is a BTA12-600C Triac, an IEC 60384-14 X2 capacitor, and both the main board and the display board have Atmega48 20AU chips.
I understand that there is some half wave rectification happening which is then controlled with the Triac to feed the heater but that's pretty much the extent of my knowledge and I'm unsure how to troubleshoot this issue.
If anyone can help me better understand what to check and what might be going on that would be great!