1994 Saturn SC2 Starting Problem

I have a 1994 Saturn SC2 with 239,000 miles. I very recently encountered what to me is a unique starting problem. Occasionally, I will get in the car and attempt to start the engine and get absolutely nothing. All electrical power has been lost. I can open the hood and push on or hit the battery and I will hear a click, like a relay closing, and find that I now have electrical power. Sometimes I notice that the domelight is dim and when I try to start the engine is hear another click and loose electrical power again. When the domelight is bright the car starts with no problem.