Well, experienced players will know right away. You hit the ball into the rail, and if it doesn't come off at a decent speed, or is different to the other rails, it's dead.
There are many reasons for one rail to be dead and others not. Most commonly, the rail hasn't been properly bolted down. You can easily re-tighten those yourself. Be careful not to use too much force, so that you strip the nut. If you have the specs, a torque wrench may be a good idea, otherwise try your best to tighten all the bolts as equally as possible. One or more lose bolts will lead to non satisfactory bounce. Another cause could be the rubber coming unglued from the wood. Carefully wiggle (without any force that could actually cause problems) to feel if this is the case. Probe it carefully like a hurting tooth, not like a gorilla trying to tear down a tree. If a portion has become unglued, it can usually be reglued without much of a problem. The cloth must be removed and replaced and contact cement used to glue the rubber back on. It's an easy diy job. Both of these will lead to the difference in sound you observed. There will be a lower pitched, kind of "hollow" sound at impact.
There are other, less common issues, that could come up with tables bought second hand. The rubber can be mounted too high, or the rail could be resting on some cloth or some other object making the rubber hit high or the wrong rubber profile could have been used. That will kill the bounce.
If the rubber/rail is too low, the ball will bounce more, and usually hop.
If the rubber and rail are on there good, then the rubber has gone dead and needs replacing. Cutting a new cushion right and glueing it all on perfectly is a bit more difficult, and depending on your skills you may want to hire a professional for that. It used to be that a pool cushion could last 50 years maybe more, but because of plastic fillers and inferior rubber, the lifespan can be as short as 5-10 years now. We have also been made acustomed to livelier rails.