Code issues causing Limp Mode - assistance req

[Shaune9]

Dear All
I have a BMW M3 E93, which I have owned for circa 15 years. The car has been garaged for a significant amount of time but well maintained.
I have recently serviced the vehicle which included a new battery, I have not registered or had this coded to the car.
When driving I now get the engine yellow warning light and the car goes into limp mode.
Using Bimmerlink the codes I get are:
• 27E4 – Vacuum pump mastervac plausibility
• 2B57 – Engine emergency program activated
• 2976 - Engine emergency program activated
• E18F – Central registry does not match target registration.
I initially thought this may be the brake vacuum sensor, which I changed and cleared codes but then they all immediately came back.
I am now thinking it may be the Vacuum pump itself, but cannot hear any strange noises, whining etc.
Can anyone please advise on their views before I have to resort to taking this to the dealer and their astronomical prices.

Please note the E18F code has only recently appeared.

[amrazM]

those vacuum pumps seize up on cars in the uk, we dont really see that problem in the us for some reason or atleast not yet. since you said the car has sat for a while I would probably start with checking the fuse for it should be F68. Then if its blown the pump is probably seized and the excessive amperage blew it. Check the brake servo unit as well, sometimes they can rust, does the bake pedal feel normal? Put 12v on the vacuum pump see if it runs.