Wait for some more people to chime in before you tow it to the dealer. I know there is software I have used to re-align the EWS system in my E36. So there must be some for the E53. I just have never needed it so I have not looked around the web for it. The one I used on my E36 I believe was called "EWSSync.exe" I just used a basic usb to obdII cable to the 20 pin adapter.

If EWS-DME sync is lost the engine will crank but fuel injection is not allowed.

Sounds more like you have problem with EWS module recognising key (transponder chip) if the other key did the same previously. With proper diagnostics you can check from EWS module what things (if any) are preventing starter activation.

I think it's more simple. Measure voltage at the jump point under the hood. If you don't see 12ish volts the problem is in the battery cable. Either the BST is opened or the connection at the B+ has opened.

What were the symptoms that had you replace the Battery?

You can confirm cable problem usually by jump starting at the B+ but you can't drive because the alternator also not connected to the battery.

If you have B+ power and the symptoms you describe it's usually the key switch. Did you have misfire starts (nothing happens when turn the key but maybe the thrird time it fires right up)? That's the telltale of key switch failure.

Everything except the alternator and starter gets powered on an alternative path which is why I suspect the main cable from the trunk to the B+

I was meaning that if you have good voltage at the battery and at the B terminal under the hood then it would probably be your key switch although I guess it could at that point also be an issue at the starter motor but Andrew can explain how to do a check of it.

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The jump start terminal under the hood is referred to by bmw as the B+ terminal.

No need to bring it to the dealer, still lots of simple steps that you can do. Actually there's nothing you can't do that the dealer can.
Does your starter have 12 volts at the big red cable?
Does the starter solenoid have 12 volts when you turn the key to "crank"?
Did you check the ground cable between the engine and chassis?

Carsoft 6.5 had the ability to realign the EWS with the DME. I used Carsoft 6.5 when I had an E34 Touring (don't call it a station wagon).

Did you try the original key?

I had this issue when I bought the battery from Sears.

Did you buy the same exact battery from the dealer? Make sure the voltage is the same or you will need to reprogram the car.

Not true - the e53 has no intelligent battery monitoring.