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; E30 318i; E32 735iL (X 2 - 1 Alpine White and 1 Glacier Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i