Bill,
It looks like you have a problem with the un-hooking slide mechanism. Either it's gummed-up with crud or you have a broken spring. Either way the gun needs to be disassembled, cleaned and inspected to find the problem.
This is a fairly common issue with Parkers. I've seen several where you can't remove the barrels with the hammers cocked, but when you drop the hammers the barrels will come right off. The most common problem I've found is an old rusty broken spring in the un-hooking slide. Other times it's just decades of old dried out grease & dirt which has it gummed up.
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