Have you shown a flashlight on the OBC? to see if anything displays. Sometimes its just a matter of the 2 bulbs that light it up. The bulbs for the blower knob and temp rotary switch are at the bottom right of the temp control panel and top left. Best to do these when you decide to check the OBC.
These little incandescent bulbs do blow after many years of usage. Either replace with new ones or maybe someone here has experimented with LED replacements?
Do you have the Owners manual that tells you how the OBC works? If not, there is the Sticky above "Owners Manual" that has a description but obviously you need to get some basic life out of the OBC first!
And I agree with the comment above about the Analogue Clock...that is what I have on my basic 318i and is much better than the electronic one I had on my 1984 323i.
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