I had a 2007 Lucerne loaned to me to go to another state next week..... I was going over it last this afternoon and found the passenger low beam was dim as was the amber parking light bulb....so I unplugged the headlight and the parking light bulb got brighter and shown as it normally does.... I put a brand new bulb in just to rule that out and it did not solve the problem...... whenever I plug the headlight bulb in the bulb is dim and the parking light bulb goes dim as well...... I've never seen anything like this..... the driver side is just fine.....................................

Check the ground circuit.

I did some more work on it today and I have power at the fuse box on that circuit as long as the switch is turned off, but when I turn the headlights on all power goes off on that circuit at the box.....additionally when the headlights are off the passenger side front turn signal works....BUT when the switch is turned on the front turn signal bulb does not work.

That'* because you have resistance in the ground circuit.
Do you know how to test it with a dvom? You can use a headlight to load the circuit as well. Look on YouTube for 'how to do a load test of a circuit' and read away.

Ah, I watched one video that told me to use an incandescent light instead of a tester with an LED or similar in it..... and I did find a problem with the ground circuit...... then I placed another ground strap on the circuit and the headlight did get a bit brighter, but the high beams still do not work and there is a problem with the blinker sill..... so I guess I'm going to have to open all the wiring (which I was trying to avoid) and find where the problem is.

You may find more than one but now you know how to load test.

Ok, this is weird and I've never seen it before, what do you think?? I did some more testing this afternoon...... when I have the High Beams on on the driver'* side that is working correctly, I have power and ground to the circuit whether on or off..... on the passenger side when It'* off I have power and gound..... BUT When I turn it on, the power and ground goes away and I have nothing a no voltage..... I turn it off and the power comes back and I have full voltage on that circuit...........................

If that were true your lights would always be on. Since that is not the case I must assume you did not test it correctly. Try again.

Headlight Off

Headlight On

That is because you have high resistance in the circuit. There'* a large voltage drop across that bad spot which is why you get what seems strange results. Experience clears up the confusion.