Judging from picture #4 this is an extractor gun, I think. Stop screw in barrel lug would suggest extractor, correct?

This is a very nice Parker. Depending on we’re you are located there may be a Gunsmith that is within driving distance of you we’re you can take it. If you post where you are located you will get some solid recommendations from members on who to use.
There are too many hack out there that will take the gun in and return it with buggered screw or more issues then before they started.
If there is not a recommended Smith with in driving distance send it to one of the recommended professionals.
This Parker has survived this long in wonderful condition, don’t trust it to a hammer mechanic.

Never attempt to seat the forend to the barrels by pushing on the wood forward of the latch. It is weakest there because of the cutout in the wood for the latch. Many have broken their forends from not knowing this.





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The easiest way I've found to get the fore arm to "seat" is to place it in position and hold it in place with slight pressure then open the action. It should snap in place with little force required. YMMV

Double Lab, thanks for the "seating" tip. I just tried that and the forearm lever does now seat, but the top lever still remains ajar. I don't want to snap the barrel shut with too much force. Thanks, Brad

Joe D,
You are correct, this gun has extractors as you pointed out, not ejectors as I had originally mentioned.
Thanks,
Brad

Brad, looking closer at your pictures I'm not convinced that the barrels are fully seated on the receiver. Try looking closely into the receiver where the lugs fit for some sort of debris or obstruction. Also look into the cavity were the extension seats into the frame.
Quick question, was the gun assembled all this time before you recently pulled it out? If so, was the lever closed, but when you opened it, it would not return when you closed the action?

Barrel Latching Closed Problem
 

Thanks for all of your thoughts and suggestions about subject problem.

The last time the gun was fired was by me probably 60 years ago. I vaguely remember the latching problem occurring then. I remember the top lever sticking to the right, and it has remained stuck that way since then. At the time, I was able to separate the barrel from the receiver and store it until now.

A few weeks ago, I got the gun out and tried to put it together. I was partially successful as the barrels would close, the forearm would latch, but the barrels would not latch shut and the top lever would not return to center position. As of today, I can remove the forearm and open the barrels but now I am unable to separate the barrels from the "receiver" (I am not sure of correct terms).

Although I am an ok mechanic, I do not really understand how the gun functions internally, and I do not have any drawings that show how the parts work together.

I am inclined at this point to let a gunsmith take a look, Although I am quite capable, I am very reluctant to start removing screws myself.

I am in Aiken, SC and the forum recommended gunsmiths, Jim Kelly in Darlington, SC and Bill Schwartz in Ellijay, GA, both of them being a couple of hours away from me.

Thank you all for your time and valuable input.
Brad Kuhn

A video On YouTube
 

Maybe this will help you out with maneuvering the pieces apart and back together.

Also an extractor gun.

https://youtu.be/cNzsWStqYtc

Brad,

Snap both triggers and the barrels should come off.

Holding the action and stock in your left hand with your thumb holding the opening lever in its current position open to the right, take a small wooden dowel and look in the center of the opening at the breech face and you will see a small metal lever down in the action. Push down on it and see if the lever releases. The trip may be gummed up and holding the lever open. If it allows the lever to return to center the you will know it was stuck. If this works you may be able to apply some oil on it to free it. Just enough to get it to consistently get it to release when the trip is pushed down by the rear barrel lug. Repeat the opening and holding of the lever and the pushing of the trip until it works every time. Let us know.