You can do a manual restart by sliding the power switch and holding it for a count of at least 15 seconds before releasing. This often clears up a lot of problems. Unplug your Kindle from everything beforehand.
If that doesn't work, I think (but I'm not sure, it's been awhile since I've done this) you can also do a manual reset to factory defaults (normally accessed via Menu/Settings) by doing the slide/hold thing for even longer (at least 30 seconds, maybe more; count ve-e-ery slowly).
You'll lose everything on it, but it should be a clean slate afterwards (if I'm remembering the correct emergency procedure).
From the sound of it, your Kindle seems to have locked up while indexing. If you put a lot of files on it (or very large files) at once, then everything slows down while it processes them for the purposes of search.
Best way to do this is to only move a few things on at once, or if you're doing a big batch of transfers, leave it plugged in overnight (indexing really drains the battery) and it'll be taken care of while you sleep.
Hope this helps.
ETA: Oh, apparently it seems they might have changed things for the DX. You should probably use the instructions in either post #9 or #13 in
this thread on resetting Kindles.
But the simple 15-second procedure does still seem to work on my K2i.