Hi, i've had ME/Fibromyalgia for the past 6 years, although only diagnosed for only the past 3 years.
I have tried many things and from speaking to many people with the same condition have realised that what works for one does not always work for another.
I am now at a good place with my condition and I have found for me walking and change in diet has helped. But the main thing that has contributed has been Remedial Massage (again this doesn't work for everyone.) I have found that when i've had a treatment it relaxes my muscles which in turn tunes in my mind. I am able to focus better and subsequently feel able to exercise.
Graded exercise is great, as long you don't expect to be able to exercise like you did when you were fully fit. I fell into this trap and you can 'burn out' when you feel well. It is hard, but if you take time to find what's right for you and only focus on one thing at a time, it may work. Again I fell into the trap of doing Yoga, Pilates etc etc, but found general walking to be great so stuck to just this.
CBT is good, but does not work for everyone.
Hope you start to feel better soon!