It wasn't doing that before, right? That means the CAS is successfully authenticating your key and signalling the starter. At this point, it sounds like you have a voltage drop problem - probably a dead battery. Can you put the battery on a charger and try again in a while? Leave the IBS disconnected.

When the IBS goes bad, it can keep the car from successfully shutting down and it will kill the battery.

As for the fuses, it sounds like they're good. At worst, they might be slightly corroded. I don't believe you could source they locally except maybe at a BMW dealer.