don't know if itouch 4 is WPA-2 compatible but my itouch 3 is not.
Your router is likely WPA-2, you can change the setting to WEP from your router i.p by typing in the router i.p in the address bar and putting in the WPA-2 code, selecting the type of security you want.
WEP is not as secure as WPA-2, you can always change it back after you are done.
If your ipod is compatible with WPA-2, which it should be as it is 4th gen and came out well after WPA-2 was commonly used, then these instructions may mean nothing.
I am only guessing your router is WPA-2 secured as that's what modern ones seem to use in my experience.
I am only saying this from memory and filling in the gaps with common sense, so I recommend using an internet guide if you are stuck.
But based on the diagnosis you gave me, your ipod touch is acting the same way mine is (it asks for a password but it seems to be wrong), and this should be a sure fire way of solving it.
Tell your parents before changing the security to WEP, you can lock yourself out of your router and require resetting! Also, any other wireless devices need to be reconnected after so don't do it if anyone's using a laptop or anything at the time.