Hello, again.
Thank you to those who offered help. For the beginner, here's what I discovered along the way:
1. Tightening the lock nuts on the sink, oddly, can affect the way the faucet handle sits. I mentioned before that I had originally thought that one was loose, so I tightened it. That action, apparently, unbalanced the faucet unit so that the handle would only spin around. Once I loosened the lock nut again (but kept it tightened just enough to stabilize the unit), the handle slipped on correctly, and is now back to turning the water on and off.
2. When you are dealing with a leak in a cheap plastic faucet, start with the easiest approach. I didn't discover what the easiest method was until I had taken the faucet apart several times. So, now I would recommend: turn off the water; put a cloth in the sink to catch screws, etc.; remove the handle caps; unscrew the handles; remove the handles; unscrew the nut around the valves; remove the casing for the entire faucet if it has simple screws like mine did, replace the nuts around the valves; turn the water back on slightly.
At this point, you should be able to see from where the water is actually leaking. Initially, I thought the valves were the problem. It turned out that water was backing up from the aerator, then running down the inside of the faucet and leaking down the outside of the pipe. I never would have seen this unless I tried the faucet without its casing.
So, after two years of struggle, I finally discovered that somehow the aerator had been misassembled. I learned from a "This Old House" video, that new aerators have flow constrictors installed in them. Mine had been installed upside down, so the water couldn't figure out which way to go. Once I reassembled the aerator in the proper direction and order, the leak stopped. Technically, I didn't need to replace anything.
I turned the water back off, unscrewed the nuts around the valves, replaced the casing, put the nuts back on (making sure the valves were properly seated in their slots), put the handles back on, and voila!
It took two days to figure all this out. The entire process could probably have taken ten minutes, if I had known then what I know now! When we got back from returning $90 worth of unnecessary equipment to the store and no water was pouring out anywhere unauthorized, we had achieved success!
Hope this process helps someone out there.
P.S. If you take the valves out, the little black rubber rings down below are called the seats. The springs that are below them go wide end down!!! Some people use needle-nose pliers to get them back in there. My fingers were small enough to fit, though. When they are in position, they have a little bit of bounce in them, so after you put the valves back in, you need to keep a little bit of pressure on them while you are re-assembling the faucet. That way, they stay in the proper position in their slots while you are tightening the plastic nuts.
), or should I try a completely new faucet?
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