i'm afraid it won't be much help, but: http://www.cuisinart.com/share/man/415_man.pdf
If you think about it, you already know the general rules of cleaning as you know what stale coffee tastes like. Blecch. Therefore, coffee grinders cannot be cleaned too often or made too clean. The general rule is to disassemble as completely as (reasonably) possible; wash what can be washed, and wipe or brush off everything else you can reach. This includes going into the spout that empties into the catch-bin with a swab or brush of some sort. Moisten your cloths, swabs, etc., in a solution of water and coffee solvent like Joe-Glo or Urnex Cafiza to do a better job.
The burrs themselves as well as the path through them needs routine cleaning as well. There is a coffee grinder cleaning product made by Urnex called "Grindz" which is supposedly pretty good. I run a few pieces of stale bread through the grind path to accomplish the same purpose. The bread or Grindz crumbs abrade off stuck coffee fines and absorb most of the stale oils. But, every so often the burrs should be removed and cleaned in solvent as well. That said, I'm not sure you can remove the burrs from a Cuisinart.
If I understand you correctly, your grinder's burrs spin without load but not with coffee in the path. This suggests it's suffering from something other than a simple jam, which would prevent the burrs from turning at all. A stripped gear for instance.
A new Cuisinart grinder goes for around $50. In the event your machine cannot be repaired for less than $25, you might as well replace it. Depending on your brewing methods it might be worthwhile to climb the quality/expense ladder a little for better quality. The extent to which an improvement in grinders increases the quality of the cup is surprising. The second biggest surprise might be that (within limits) grinders make even more of a difference than brewers. Without knowing how you brew, it's not easy to make the right recommendation. Perhaps something like a Baratza Maestro (~100) would suit you. It's a good choice for "French press," vacuum brewers, and better filter makers. If you're making espresso with a real machine, you need something significantly [gulp] more expensive. The rule of thumb is 1/3 the cost of the espresso machine. On the other hand, if all you drink is coffee made in an average automatic drip machine, a simple $25 (SURPRISE!) will do the job as well as anything else.
Hope this helps,