I found out the problem: I used the wrong Logic Board! I have a 5th Gen. 80GB model and needed the 820-1975-A board (instead I installed the 820-1763-A board, which apparently only works for 30 and 60 GB models).
I got software problem after installing new Logic Board. iTunes keeps asking me to restore - I do, but it make no difference. Still can't synch. Anyone else have this problem?