I have an older K Frame 38 revolver that binds up or completely fails to engage the hammer in double action, single action functions just fine. I opened the side plate to observe and the trigger binds in the hammer sear. If I apply a slight pull pressure to the hammer, as if to cock in single action, the binding stops and trigger pulls as it should. Any suggestions?

If you able to do so, a thorough cleaning and re-lubrication of each of the internal parts and the internal frame area under the sideplate would be a good place to start.
Sounds like the action may not be fully returning into battery when you are releasing the trigger. This often results in the sear not returning fully forward..... resulting in the sear not being in the proper position above the trigger step when the trigger pull begins.

You might also check the rebound spring to see if it is a full length OEM spring. It may have been modified (cut) or a lighter spring substituted by a previous owner.

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Ret. LE, FA Instr, S&W Armorer

If you haven't done it before it sounds like what is needed is a thorough cleaning and oiling! This means everything!!!!! It seems many people don't realize mechanical devices require periodic lubrication!

After re-reading your post there is a second issue. Let go of the trigger in double-action! The most common reason for what you describe is operator error in not allowing the trigger to fully recover by keeping slight pressure on the trigger. This can be exacerbated by a rebound spring that has been cut to reduce trigger pull, or replaced with a lighter that factory weight spring without understanding the necessary balance between the rebound spring and main spring weights. A very common problem when people who do not understand the mechanism ant think they can simply change springs without seriously affecting function. To check the rebound spring simply take it out and look at it. If it is a factory spring and does not have a closed coil on both ends then it has been cut!

And, BTW, still give it a thorough cleaning!

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Gunsmithing since 1961

While a thorough cleaning and lube is definitely the way to start (first thing I do when a gun is acquired by me), I'd suspect that you have something poorly fit or broken inside. Could be a problem with the DA sear, or even a broken spring. When you open it up to clean and lube, all parts should be inspected carefully. If you are not knowledgeable and or mechanically inclined, a competent local Gunsmith would be the place to bring it.