Htc Rhyme Wont Play Entire Notification Sound?

1. If you can;
than the inner-speaker of the phone must be damaged. You have to take it to service.

2. If you can't;
you're either on vibration mode(which you say you're not), or a software error has occurred. Try these:

2a. Soft Reset
Press and hold the Power button for about 10 seconds. This will force the device off. The screen should eventually go black and power off. Wait a couple of seconds, then press and hold the Power button to try to turn the device back on.

2b. Hard Reset
There are two ways you can perform a hard reset.
Option 1 – Using the OS menus

Select Settings > Storage > Factory data reset > Reset phone > Erase everything.
(You might want to back-up your memory before resetting)

Option 2 – Using the hardware buttons before boot

1. With the device off, press and hold the Volume Down button while turning the device on.
2. Continue to hold the Volume Down button until you see 3 Android logos.
3. Use the Volume Down button to toggle the selection on the screen to Factory Reset. Press Power to make the selection.

Thanks