Take a look at where the traces from this inductor lead.
If it’s a 6/8-pin +12V connector for the graphics card, then there’s no problem.

My apologies, I wasn’t paying attention.
This is clearly a high-current inductor with a resistance well below 1 ohm.
If the coil is broken, it needs replacing.
Some thing like thats https://imrad.com.ua/ua/jrpi0604m-r82m-586368
If only the core has snapped off and it’s located right at the connector’s input, it can be glued back together.

1 I dont see crack on the picture?
2 https://www2.vgamuseum.info/index.php/f-naq/i … -radeon-hd-4890
3 If its the ferrite part cracked then yes you can glue it up. Think of it like a broken magnet - stick two pieces together and it still works like a magnet. Or like electric motor stator/transformer core - build from individual slices of steel to reduce Eddy Current losses.

4 R10 inductors in this card are used to filter incoming 12V.

>coil itself isn’t shorted

5 Yes as shevalier said coils/inductors are MEANT to be shorted 😀 if its not reading short then its open aka broken 😀