[BrotherRob]

The beeping sound makes me wonder if you have an alarm system that reset itself when the power was disconnected. You might search factory alarms and see if you can find a control box. An alarm shouldn't put much stress on the electrical system but likely has an ignition kill.

The meter on the dash is a voltage meter. It will display the battery voltage before starting. It should increase notably after starting and then settle to a level slightly above the starting voltage while the engine is running. Its not a precise tool but it can give a ballpark idea of what's happening.

I would continue checking the battery especially in the evening and after sitting overnight. See if its holding or loosing power. That will narrow down the possibilities. If you've not done so, make sure all the connections are clean and tight.

Was your HG done in a shop? If so talk to them about the symptoms. Find out what connections were disconnected, altered or possibly damaged.