As deadin states, something is not functioning correctly, probably due to parts wear. Pull the trigger through using the double action mode. After the hammer falls, keep pressure on the trigger and try to turn the cylinder. If it clicks into battery, the hand is not pushing the cylinder far enough. Second, try the single action mode and do the same thing, plus make sure the cylinder does not wobble or have any side play while holding the trigger back. Lastly, is there any hesitation while the hammer is falling? Sometimes, due to internal wear, the hammer will catch and therefore not drop freely or drop before full cock. In DA mode, as the trigger lets the hammer go, there should be no interference and the hammer should fall freely from full cock.
It is not necessarily easy to determine which part is out of spec and also hard to find good quality parts for these revolvers. Unless you are well versed in gunsmithing, I would try to find a gunsmith that has experience with these old DAs and get an estimate for repair. Good luck and hope you get your 38 back in working order.