We had a pair of D3's until I managed to unload them on some poor unsuspecting soul. There are heaps of issues with the early D3's and hopefully some of them have been sorted in your newer model. Whilst most things should throw a fault code, the things I have experienced that could cause your issue, and are known problems, are - bad wiring loom connectors where it connects to the ECU, and bad crank angle sensor. My first guess would be the crank angle sensor. Did the mechanic confirm that the injectors are actually firing, or just bleed them? These are not like old school diesels, and you might have fuel in the rail but still get no injector fire.
As a quick aside, when your turbo starts giving problems and Volvo tell you that you need a new one for $1000's, note that the most common issue is the variable vanes getting sticky and that it is a reasonably easy DIY job to remove the turbo and clean the vanes. Costs a couple of hours and a new gasket or two.Takes a while the first time, but I got pretty quick at it after we spent $1000's replacing the first one at Volvo's suggestion. You should also carefully inspect the main sea water hoses. It should be sorted by now, but many early D3's came out with the hoses installed such that they rubbed on the engine mounts or exhaust system and would rub right through if not checked in time.