You can check if the immobilizer is interfering with most of the BMW scanners out there. Although on all the BMW’s I’ve ever seen with immobilizer issues, they wouldn’t crank at all. Can you scan data from your crank/cam sensors? Presuming you have the proper fuel pressure (don’t assume because its there, that it’s enough) you now have to confirm spark & then compression.

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Current vehicles
2001 325XI
2006 X5 3.0
2004 X5 3.0