I agree that seat post and whatever is going on with the binder need to be sorted out first.
A Columbus sticker doesn't automatically mean a full Columbus frame/fork. Bianchi was using a lot of TreTubi Columbus and Falck stay and fork frames during this time so it stands t reason Trek may have been doing similar things.
No crank or wheels? What else is there? Does the stem move?
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk