Dumb question! You mention, fuses are good..... Did you check
ALL your fuses.....looking in my Bentley Manual...
there are 9 fuses connected with the OBC......ready......fuses- 11[7.5A], 12[7.5A], 23[5A], 27[5A], 31[5A], 33[10A], 37[10A], 45[7.5A], 46[15A].
No.........
keyless entry on most e36's, are of aftermarket production......
jb