I dont know how much this will help but here is what happened to mine.
I have a desktop with windows and a macbook pro. i always used the pc for iTunes since i had it when i got my ipod. I tried to restore my ipod but it wouldnt show up on itunes. after i got it to show up i got the error 1621, like yours. i plugged it back into my pc and it restored fine. the only things i would think it meant is that i was restoring it with a different computer than i set it up with, or because i was restoring it with a mac and i set it up with a PC. i never found out what 1621 meant.
sorry if it doesnt help, thats just what happened to me.