A diesel will run on cat poop once you get it started, so yes it will run "OK" once warm even if the injectors are bad. Testing is probably as much as replacement, they sell new ones here and I sell new ones.

Removing the starter is no a big deal but the best way to test it is on the car.

You need to find out if lowcompression is your issue.

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1971 Porsche 911 Targa RSR rep.
1968 BMW R60/2
1981 BMW R80GS-PD, dual plugs, 1000cc jugs, 10 gal "Gaston" tank.
1982 BMW R80GS-PD, duplicate of above.
1988 Neoplan/Mercedes 40' Bus
2002 SLK32 AMG
2013 Smart Electric