You don't have to not move, you just have to not carry out any sort of activity. It's not a case of staying completely still. Wake up and do nothing (activity wise) for a few minutes and see if any fragments come to you. Search your thoughts. I have no doubt that when you sort your sleeping pattern out, you will recall a lot more. How much sleep did you get last night?

If you still have trouble with recall after that, then you should maybe try using mantras to help you out to remember them. As you're falling asleep say something like, "I wake up and remember all my dreams," in your head over and over again. Try and have it be the last thought as you fall asleep. This will help you out a lot, and it's how I got my recall up initially, and if it dips, I still use this to help me out! Remember that it may take a week or two to get your recall up to 1-2 dreams a night, especially if you have none at the moment. Keep on going and don't lose hope! It's a hard journey, but it's worth it! Good luck!