[knt]

Might be worth a try resetting the ECU

MINI Cooper ECU Reset Procedure - R50/52/53 MINIs

MINI Cooper ECU Reset Procedure - R50/52/53 MINIs, lean from the experts at Mini Mania.com

new.minimania.com

Might be an electrical short somewhere, but tracing a short will be long and difficult process.

Might be worth installing a car battery Isolator.

 

[knt]

Check the ground wires is connected properly and/or not rusted.

1st Gen - R50 - Cooper - Gen 1 Ground locations in engine bay

Where are some of the more common ground locations within the engine bay?

www.motoringalliance.com

Might be other ground locations worth looking at.

 

[knt]

If you've checked the ground locations then try checking the relevant fuses etc...

Fuses, Relays & Earth Points

Some useful electrical info listed in one place & hopefully easy to search:- (please feel free to add more or correct any errors) MINI Fuses / Relays / Earth Points Engine compartment fusebox F1 5A Digital engine electronics control unit F2 20A Digital engine electronics control...

www.mini2.com

The BCM could also became faulty after the loose battery terminal.

MINI Cooper Driving Light Installation (R50/R52/R53 2001-2006) | Pelican Parts DIY Maintenance Article

One of the most popular modifications to the MINI is the addition of a set of driving lights. In this article, we have added tons of photos to show the whole procedure.

www.pelicanparts.com