On the 1st Gen there is the plastic with a small metal u shaped piece that has a spring metal contact on it. This is screwed onto the metal case. It can be replaced but I have not found a vendor who sells this piece.
There is a gold clip piece that presses down on the front of the case and can get lost easily as per other posts on this site. It is referred to as an antenna but I am not sure what exact function it performs in the antenna circuit. I think it provides some sort of ground to the circuit board and to the metal case. I have not found a vendor source for this either.
The actual circuit board side which is rectangular looking with one rounded side and has copper traces on both sides is an integral part of the whole $100.00 plus I pod circuit board. I wish just this small circuit board could be replaced but it looks to me like it is a ribbon cable sandwiched inside the main circuit board.
Maybe the spring contact on the plastic small metal u shaped piece could be pushed down and needs to be extended again to make contact with the copper circular land on the small circuit board. Or maybe the gold clip is out of place or case is popping apart or the iPod got dropped at some point of time and the spring clip or some other mechanical connection got out of alignment.
There are pics on the repair site that show the parts I am referring to and also a post below about the mechanical issues.
Good luck as I am fighting the same wifi issues on my 8 gig with less than reliable success.