2000 Chrysler LHS

Question
I have a 2000 LHS that has just started showing electrical problems. These all started as it got cold in WI this winter.

1. Put key in ignition and turn. Dash lights start bright, then cut except for OIL light which flickers in time with a ticking sound which gets faster until all the lights pop on and the car starts as normal. This has happened 5 times in 2 weeks.

2. Radio sound wavers, or volume fluctuates downward randomly and/or in time with other electrical event. For instance if this waver or volume fluctuation shows up and I flick on my brights, that will cause a volume fluctuation. The windshield wipers also seem to sometimes effect this volume thing. This has shown up on two occasions both about 20-30 minutes of driving.

3. Trac Loc/Anti-Lock breaks have died on me one time. This was at the start of a long drive that ended with the volume problem. The light for TRAC LOC OFF when on without me pressing the button. This was immediately after starting (and having the starting problem described in #1.) It was a snowy day and trac loc would not work and the anti-lock breaks also were not functioning.

4. Last night while driving (end of 30 minutes of driving) all of my power systems died for about 1 second while I was driving. Lights, radio, dash, headlights. They all came right back on and the car functioned normally.

The car has 350,000 miles on it and otherwise runs incredibly well and has been low maintenance.

Any help would be greatly appreciated.

Thanks in advance.