I realize you mentioned you had your battery & alternator checked, but this sure sounds like a battery problem to me. If you had your battery & alternator checked by someplace like AutoZone, I'd try test #9 on your instrument cluster, or, use a multi-meter on your battery, just to double check.
2000 740iS. MKIV, 16x9, DDEs controlled by Euro fog light switch, reversed steptronic +/- pattern, paddle shifters, clear corners, Basslink, iPod video with stereo audio, TV tuner, gauge rings, ///M pedals, backup camera with 'on demand' switch, quad brake lights, Dinan engine & tranny software, windows/sunroof close via remote.
2003 540iS. MKIV, 16x9, PDC, CWP, TV tuner, backup camera with 'on demand' switch, paddle shifters, windows/sunroof close via remote, iPod video & audio.