My bmw 320i e90 2005 only cranks but won't start

USA CAR,NOT tOLD yours.nor "e"code, series3 code.
e21 ,1975?
2.0L
320i. the "i' only means fuel injected 320d is diesel
what matters more 'e" code, e21 up.
No year told,
NO ENGINE told, nOR GAS OR DIESEL.?????? i= gas.
first we test fuel last , not pumps first (sorry but i cover that)

the engine must be good, no bad engine burns fuel and run.
next is (gas engine) spark must be good or if diesel glow plugs.working.
then comes fuel checks last. (all this is basic basics 101 stuff)
the PCm cuts fuel for many good reasons.
but we test fuel pressure cranking, on any dead engine using a tool called fuel gauge ( PSI or in Europe BAR/kPA)
CRANKING ONLY
IF THE FUEL PUMP RELAY IS DEAD, MOST TIMES THAT MEANS
THE PCM IS CUTTING FUEL ON PURPOSE.
TOP CASE PCM SEES SPARK DEAD AND MUST BY LAW CUT FUEL FAST.
if car has bad TPS sensor and it sends 5vdc to the PCM for throttle angle (100^%) or WOT false signal the PCM cuts fuel
or the PCM sees IMMO not happy it cuts fuel. or spark and on some cars even cuts cranking, on my car it cuts fuel after 3 second run
if IMMO KEY FAILS.

other simple tests, is Test fuel.spray
if engine good and spark good, test fuel works.
see? but no engine told
and spark plugs all tested for good spark..
on on all uSA cars here, 1996 up any OBD2 scantool works
so we scan it first. see why the PCM cut fuel???
as it can for many reasons,
on gasoline engine top causes are P03xx DTC errors
for sure CMP or CKP sensors failing it cuts fuel 1or2 ways.

NO CAR TOLD at all.
47 year span , sorry can not guess.

The year the first BMW 320i was manufactured was 1975
Max Nebular car.

fuel is cut to prevent CRASH and burn as seen on TV, endless.
by law and pure hard LOGIC. deep inside the PCM.
and more.

Have you replace the fuel pump relay?

Relay, on top of fuel tank under parcel shelf, check its getting power, if not its fuse, if it is, bin it get a new one.

I believe you will have an issue with your injectors. Check your mileage with the manufacturers recommendation on replacement.
Before you do anything, just put into your fuel tank a SLICK 50 Fuel Treatment Additive - half tank of petrol - and take it for a good drive. Read the directions on the box. Probably solve the problem for the time.

You might have a defective fuel tank pressure sensor!

Fuel Pump or starter. Since you say it's turning over but won't start I'd say it's your fuel pump. You'll probably have to drop your gas tank to fix this problem as your fuel pump is in the tank. You might be able to just loosen the straps and lower your tank a little to access it without removing the whole tank. Check around to local junk yards for this part and you'll probably find it for half the price as new. Make sure you can get your money back if the used pump doesn't work before you pay for it though. Don't forget to run fuel system cleaner (2 bottles to a full tank) once a month.

Check your fuel filter if it needs replacement. Empty it out then connect it back. Try to start it again. Inspect the fuel filter if it filled with gasoline. Check if there is noise at the fuel tank to check if the pump is working. If it did not, inspect the fuse for your fuel pump and the relay. If both are good you may connect the fuel pump directly to the battery to see if it works. It may be a bad wiring.

Has the fuel filter ever been replaced? Instructions are here. http://www.frontiernet.net/~papi/Filter.html
This car has two gas tanks, one on either side of the spare. The fuel pump that delivers fuel to the engine is on the right-hand side. When the left tank is less than half full, it requires a transfer pump to move the rest of the fuel over to the tank with the fuel delivery pump.
Those transfer pumps sometimes fail, or can simply come loose. When that happens, the car 'runs out of gas' though it still technically is one quarter full of fuel. It cannot access the rest of its fuel. This happened on my bosses '03 325 a few months ago.
If this is the problem, you can be sure to keep it more than half full of fuel until you can get it in to get it fixed.

sounds like the fuel pump in youre fuel tank at fault try hitting the tank whilst someone cranks the engine ensure its in neutral and cant roll away if it then starts you will need a new pump