Just to add my own contribution to this thread, I just finished fixing my daughter-in-law's DC14 with a brush that barely turned and touching virtually anything would stop it.
After disassembling the brush, it was very apparent that the belt going from the motor to the clutch was very worn and stretched and wasn't able to transfer power from the motor to the clutch. The clutch itself was fine, so I ordered a pair of belts from Amazon; the belts were $6.50 USD vs. about $40 for an entire clutch assembly.
[link|https://www.amazon.com/dp/B01FUEZI16|Amazon.com - First4spares Vacuum Replacement Clutch Belts for Dyson DC04, DC07, DC14, & DC33 Only Vacuum Cleaners (Pack of 2) -|new_window=true]
And since there wasn't a decent iFixit-style guide that I could find, I watched enough YouTube videos to get the hang of it, and wrote my own. It turned into one guide for replacing the entire clutch assembly and another to continue on and replace the belts in the clutch assembly, which didn't turn out to be quite as bad of a job as some comments and articles made it out to be.
[guide|161794|Dyson DC14 Clutch Replacement - iFixit Repair Guide|new_window=true]
[guide|161796|Dyson DC14 Drive Belt Replacement - iFixit Repair Guide|new_window=true]
So, anybody needing to do either of those repairs, here are the guides for it.