Sounds like a battery voltage problem. This does not necessarily mean the battery is the problem. There are numerous connections necessary to get the battery hooked to the systems involved.

Because of the diversity of systems involved it would be likely that the problem if not the battery would be close, in the primary power distribution ciruitry - battery cables, alternator harness, accessory leads to inside.

The alternator could have been involved with depleting your battery but has no part in the current situation. Without a voltmeter to trace the drop, one might wish to try another battery.

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Steve Brotherton
Continental Imports
Gainesville FL
Bosch Master, ASE Master, L1
33 years MB technician