While replacing a GFCI I find it has 2 circuits running into it. New GFCI trips
Modern GFCI devices will not set if the LINE and LOAD are reversed. If there's power on the LOAD wires, the device will not (and should not) set. It sounds like the GFCI is working as designed.

You're going to have to figure out how both circuits are wired, to determine if this is intentional or accidental.  If it's intentional, you can simply cap one set of wires in the box.  If it's accidental, you'll have to disconnect the crossed wiring, and then connect the LOAD wires to the GFCI.