The actual safety assembly in a Parker is pretty stout and not easily damaged. Your description is a little hard to grasp at what exactly is going on and what could be the problem.
It is pretty hard for things to not work unless, as others suggested, your stock head is coming apart. Since the whole deal is housed in wood. Any change to that can create problems.

I agree with Brian, likely a wood problem. But try the screws if you have the correct drivers so as not to bugger them. Tightening them won't likely solve it, but as Dean said if the tang screw is too tight it can bind it up, but usually it won't work in hand then either.

Thank you for the recommendation of Northern Virginia Gun Works. I dropped it off on Monday afternoon and Sandy had it fixed by Tuesday afternoon. Great job and not bad on price. You were right on the wood being a problem. Surprisingly, it is the original stock and a piece had broken in the stock head holding the bar in place. He added some glass and it works just fine again. I’m ready for hunting season:)

It may not be a bad idea to get a staple in the head of that stock to prevent farther damage. And also trying to get all that inletting sealed up would be good.

Brian, much thanks for the good advice. Sandy did such a good job with the Parker, I’m going to have him repair the LC Smith safety, which he said he is able to do, and return the gun to the field on pheasant. Ahhh, I just love fall.