I was planning to start either Atkins or Dukan yesterday, but it's been so stressful at work the past few weeks that I lost all my motivation and started eating burgers and ice cream instead. How do you normally deal with a situation like this?

Sorry that you lost your motivation. It can be really hard when that happens I find that it helps to make a plan the night before of what I'm going to eat the next day and even a few days in advance. It can help deter you from being tempted to eat other things.
Good luck for getting back on track

I usually just set a new start date and then go from there. To be completely honest, this is something I struggle with, too. If it's not an issue of motivation, it's an issue of using food for comfort.

It's tough dealing with a diet when you have so much work stress. It might be ok to just plan what to eat tomorrow only.

Somethings you like but are healthy.

Stuff that works for me are:
porridge or eggs for breakfast
Sandwich, Soup for lunch
Fish/Chicken with some veg for dinner
Drink plenty of water
Eat a couple of pieces of fruit
Desert - have a couple of scoop of ice cream!

Remember that lack of sleep just makes stress worse so watch that.
Doing some exercise can be a better way to cope with stress rather than eating fatty food.

All in all, be good to your self.

Hope this helps a little bit,
Rory