When starting only short engine rumbling, but engine does not start

Hello Together, My Ball no longer wants to :‘-( Vehicle data: SMART CITY-COUPE 0.8 CDI Key number: 8773 302 Built: 07/2002; approx. 160,000 km When ignition is switched on, you hear a surging noise (fuel pump (?)) for a few seconds, while switching to N you hear the gearbox. When starting the starter spins, then the engine rumbles a few times unround before it goes out again. It sounds like the last kick is missing so that the engine runs round. This can be done until the battery becomes weak. 1. fuses are checked; all are OK 2. gears are heard when switching on N, R and 1 3. New battery installed 4. start pilot/start assistance spray: Just as described above. Engine jerks a few times, but does not pull through 5. relay box climate (under driver’s seat) reinstalled 6. high pressure pump approx. 1 year old; pressure according to Bosch reader 350 bar 7. error indication lt. reads: charging air cooler, gear selector not gear lever position?