The fact that you are able to write a thread that makes sense and use good grammar gives me the impression that you also care for your Vacuum (Even though it is a Dyson) so I assume you clean the brush roll regularly? Every one to two weeks per say? If you don't it can cause it not to spin and as mentioned above that WILL make it very hard to push especially on higher pile carpets. I personally recommend cleaning the brush roll every other use to obtain maximum performance with every use!
However, you say you have taken it to a shop to be serviced, I expect they left it in the corner while they drank tea and waited for the next fool to walk in so they can take their hard earned cash also, but lets assume they actually serviced it and in which case it should be in perfect working order. Have you tried it on other carpets? For example, you say you have 2 new carpets which have caused this issue but how does it perform on the old carpets? That is assuming you have more than 2 Carpets in your home, if you don't then you can't do that experiment, sadly.
If I were you I'd use my common sense and simply visually check everything, make sure the brush roll does spin, and keeps spinning once it hits the carpet. Also bare in mind, if your new carpets are higher pile then your old ones it will require more force to push over them, that is THE only thing I liked about the Dyson I had, it was very satisfyingly hard to push on my particular carpets.
As for the Dyson engineer, he'll do what you would if you was to do what I mentioned above ^^^ look at it.
I hope you fix this yourself and don't have to spend your hard earned cash.
Have a wonderful night! (If you can sleep knowing your Dyson and carpets don't like each other)