After spending hours on Google to research this question, I have come to the conclusion that I'm stuck with one of those quirky Windows problems that affects some users but not all, and for which there is no established cause or cure. (And ToggleKeys is not my only problem - see below.)
For most users (I presume), the tones made by ToggleKeys play just fine. But for many other users - including me - they do not play at all. For some users, ToggleKeys has to be turned on with every re-boot. Other users need to check both Turn on Toggle Keys and Turn on Toggle Keys by holding down the NUM LOCK key for 5 seconds to hear the tones. Some users can only hear the tones when they use their on-board sound controller; others can only hear them after installing a sound card. For some, updating or rolling back sound drivers fixes the problem, but not for all. I don't have enough information to say whether this problem affects both 32- and 64-bit versions of Windows.
I was hoping this might be a hardware problem - they're often easier to fix. But, unfortunately, this problem manifests on different hardware setups: desktop and laptop, sound card and sound chip. And in every case where this problem is found, all other system sounds play perfectly well, as does music.
There is no explanation for this (or if someone knows the explanation, they aren't telling) and only one workaround: There are third-party utilities that replace and extend the functionality of ToggleKeys.
For those with working ToggleKeys tones, here's a tip: Microsoft decided to send the tones to the system's external speakers (or headphones, as the case may be) instead of using the motherboard's built-in speaker (the one that makes 'beeps') as in Windows XP. So if you're working late at night and mute the sound so as not to disturb your family's sleep, you won't hear the ToggleKeys tones.
As I mentioned, ToggleKeys is not the only quirk I have to deal with. I also discovered that Narrator doesn't work at all. It doesn't read anything out loud, so matter how high the volume. For me, Narrator is just a novelty, but still: why doesn't it work? It worked perfectly in Windows XP.
In researching my Narrator problem, I learned that Narrator is a test-to-speech utility, so I immediately went to the Speech Recognition control panel and the Text To Speech tab, to see if that functionality was working. When I clicked on the Preview Voice button, Microsoft Anna didn't say a word. Eventually, an error message appeared:
"The requested task cannot be carried out because the necessary engine could not be created. Please select a different engine and/or a different audio device."
It turns out that this is another one of those quirky Windows problems for which no one seems to have an explanation or a resolution that works for everybody.
To put things in perspective: Windows 7 also has many, many improvements over Vista and XP, and I'm grateful for that. But the new OS also removes and breaks (in this case) features that worked perfectly well in XP. What's particularly surprising is that Windows 7 breaks accessibility features. Many businesses, public institutions and government agencies are required by law to provide computers with accessibility features.