If the CPS is a dead end go back to basics with the battery terminals, cables, earths and connections. Could be you missed something. No point in buying a parts dept to fix a bit of corrosion on a terminal.
Good - Fast - Cheap: Pick any two.
E23 735i; E32 735iL; E34 535i; 2 X E38 735iL (Oxford Green and Alpine White); R50 Cooper; R55 Cooper Clubman.
E21 318i; E30 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i
I've just changed my wiper blades and now my reverse lights don't work. Should I change my fuel pump relay?