Hi,
Low compression does seem like it is your issue on this M54 engine. However, I have not seen the oil pump sprocket falling off causing low pressure then a lifter issue, then a no start due low compression. Normally, that gear doesn't fall off all of a sudden. The nut normally comes off and the engine starts running very poorly due to low oil pressure causing lifter issue.
Has the vehicle been sitting a while or not run in a little while?
Here is a video of a more common cause of low compression on these engines:
https://youtu.be/NtsKiKWeoa0
If this is not your issue then you will need to run a leak down test to try to determine if the engine is sealing and if not, where you are loosing your compression.
Here is a picture of how the nut will fall off the oil pump gear.
Let me know what you turn up with this video or the leak down test and we can go from there.
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Friday, June 21st, 2019 AT 5:10 PM