318I Electrical Problem

I have a 1993 318I Sedan. I am experiencing a problem in the electrical system. The A/C compressor will cut off (blower motor doesn't), the ABS warning light will come on, and the dash illumination lights will go off.
All of this occurs at the same time. They may all stay off for a few seconds to a few minutes. I have searched for a faulty ground, with no luck. Any help would be greatly appreciated. Thanks
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