iPod touch not working

I get the feeling that you did not search and that you disconnected early.
I have to ask, you did reconnect it to your computer right? What did your computer do (when you connected it)?
If you searched for un-bricking your ipod touch you should find some very useful things

 

You should be able to connect it and restore. Weird!

it's probably not bricked. it's just being picky.

 

Plug it in, and it should ask you if you want to restore it. If not, find the iPod on the left pane in iTunes, and click it. Then find restore.

 

^^ What he said.

If it was bricked the iPod wouldn't be responsive at all (by that I mean the screen wouldn't even display anything). That screen your describing means that you need to connect to iTunes (hence the cable pointing to the logo) - plug it in and it should tell you that you need to restore in order to use the iPod.
It doesn't have anything to do with unplugging it during a sync, if that's what you did it'd merely be have the same stuff on it as before the sync