Not sure why the on-board computer would not work anymore.
The dashboard indicator lights will still work with the new motor.
As a general rule I change the oil every 6K miles or 6 months.
I only use Synthetic, Mobil 1 0W40 (I buy it at the mercedes dealership)
I also change my own oil and reset the computer myself.
I have two BMW's and the Dealership has not seen either of them yet.
Find a good mechanic that works on BMW's, (if you ask other BMW owners someone will know the BMW guru in your area) much cheaper and better in the long run.
Stealerships have huge overheads and must constantly overcharge to stay afloat!