If it's an old DC07, you may have an old pattern cyclone, which was prone to clogging.
With the dust bin removed, look up from the bottom of the cyclone assembly thru the central tube (torch is useful) You should be able to see all the way to the top.
Ours was stuffed full of dust.
I rang Dyson and got hold of someone technical. Briefly explained the symptoms and described what I'd found.
Despite the machine being out of warranty, Dyson sent a new cyclone FOC.
If you squint up through the outlet hole at the side of the cyclone, where it joins the suction port on the body o fthe vacuum, you may just be able to see up into the tine port at he bottom of one of the 8 cyclones. (Small dentist type mirror useful)
Our old one had a small bar across the mouth of this port. I think it was supposed to start a switl.
The new one didn't have this bar, just a series of tiny grooves up the side of the port, which I suppose does the same thing.
Last bit: If your motor does pack up (and they do run hard to suck like that) it's just as cheap to get Dyson to do a fixed price service for £65 (feb '08) as it is to spend £60 on a new motor + post-motor filter and do it yourself.
I had a Dyson service and ended up with £120-130 of bits fitted for my £65.
Hope that helps
John, February 2008