12.4V indicates a bad cell. Not enough amps to power major equipment. I would assume the battery is toast.
Check fuse 11.
Can you reach the EWS module? You can test for power at this location. The two large wires are crank power. Disregard the fuse. The fuse is a bypass for EWS. EWS has to be coded out so it will crank. I did the mod to my mine temporarily. An ECM with EWS deleted allows the bypass for cranking.

Can you supply power long enough to synchronize a key to EWS? It might work to crank it. Are key batteries okay?

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'06 X5 3.0i - bought @143,123 miles (12/26/20)