E39 525d issues in 2001

[madmadmax]

Hello, I just got an e39 525d (with what seems like an M57 D25 engine) and it's not running well. Even worse, there are occasions when the engine is warm and turning the key backward won't start the car, even though it usually trembles violently and makes a fairly awful noise while idling. The engine needs to cool down, which could take an hour or two. What do you think about that? Is it necessary for me to invest in diagnostic tools? Thank you ahead of time!

[Diveintothebluee]

Administering injections.
To identify the subpar ones, conduct a leak test.

[madmadmax]

Along with Carly, I performed a scan, and the results showed the following engine module errors:
Option 1E30: Boost pressure plate or boost pressure control
1E25: Speed sensor monitoring
3505: System with glow plugs

It has an exhaust leak, which could be the source of the shaking (though it doesn't happen every time), and I also found out that most of the exhaust silencers aren't working.

On the other hand, I can't say for sure that these fault codes are accurate; on multiple occasions, I had to use jumper cables connected to the battery to get the vehicle started again.

[Diveintothebluee]

Have you checked the injectors for leaks yet?

[Diveintothebluee]