transaxle on 2004 Chevrolet Venture

It does not shift into gear. The shifter just moves freely, looked under hood and the arm is not connected to something which is what i need the name of the part

The shift control cable in your 2004 Chevrolet Venture van connects to the shifter inside the van - which seems to be working. The other end is connected to the transmission shift linkage. The shift cable could either be disconnected from the shift linkage or the cable retaining bracket, you will need to look to see which.
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go to a junk yard they are cheap and you can learn how to remove the shifting lever cable