You don't have a 20 pin DLC based on the build date you gave....that's why you can't find it. The engine bay DLCs ended with the 9/00 build date for the e39/e53...and with the 6/00 build date for the 3 series. The e38 & Z3 are the only models at the time that still received the engine bay 20 pin DLC due to them being near the end of their production run.
You also took the battery registration wrong, too. It's the new gen BMWs that have iDrive that require battery registration. The e65/e90 models have the BSD communication bus, then starting with the e60 in 2004...each new model received an IBS (intelligent battery sensor) and the battery info is communicated over the LIN bus.
The e53 has neither the BSD nor LIN...or IBS...it falls under old generation BMWs where you can just replace the battery ( correct size of course) which would be a 49/H8 battery class size.
