First and foremost: FLASH DRIVES ARE NOT FOR BACKUP. They are highly volatile, sensitive, and picky about -everything.-
That out of the way, don't turn that computer back on until you're ready to go with some recovery software capable of performing raw linear data reads. FileSalvage was always my favorite under OS X. Do not make any attempt to boot from that hard drive until -after- the recovery is performed. Doing so has the potential to overwrite the "missing" data and make it irrecoverable.
As for the flash drive, why were you using copy/paste? In future, drag and drop. That way you'll have visual cues as to what operation is actually being performed. Macs are picky about third-party filesystems (FAT and NTFS, specifically), and read/write errors are quite common with the former, while the latter remains read-only, unless Apple has paid Microsoft a hefty royalty.
In the mean time, the flash drive is junk. You can try enabling hidden files on the Mac, then browsing through the flash drive to see if there's anything left on it, but chances are nothing ever made it.
As to what happened? God only knows. Without being there to poke at the machine, see the configuration, and test some stuff out, all I can give you is speculation. I personally haven't seen this issue since OS 8 and floppy disks. Here's one possibility: If the files were originally on the flash drive, then moved to the desktop, they were never copied to the computer. OS X maintains a "desktop" for each removable device. While the files may appear on the desktop, they're never actually copied over to the host computer. This can create some confusion for the user as it can be difficult to tell what's really where, especially when trying to make copies. If there was an internal power fluctuation, or if the flash drive was removed improperly, then it's possible any actual transfer that took place may not have completed properly, or was corrupted upon improper removal. Again, if the flash drive was formatted in a foreign file system, this compounds the problem significantly.
If you have any more information you can provide about what happened, I may be able to provide a bit more insight, and offer further suggestions, but as it stands, it's quite likely the data is gone. :-[
