I seem to be unable to use the keyboard shortcut ctrl+3 to hide a selection inside of Adobe Illustrator. Ctrl+2 for lock seems to work fine, but ctrl+3 doesn't do anything for me. Selecting 'Object' > 'Hide' > 'Selection' does work, though.
Ctrl/CMD 3 using the standard keyboard and not the keypad most certainly does work under normal conditions. It sounds to me like there is another operation on your computer that is taking precedence. If you're on OSX then you can investigate the keyboard shortcuts quite easily in the System preferences keyboard panel. If you're using Windows (which it sounds like you are) then you'll need to hunt down what piece of software is "stealing" the shortcut. Try running Illustrator without anything else running, including applications that reside in the system tray.
Have you also tried editing the shortcut to another keyboard modifier to see if it will work with an alternate combination? If the hide function fails to work even when the shortcut is changed then there is certainly something peculiar going on with your Illustrator setup.
To diagnose this you could try resetting its preferences as a last resort. You do this by starting the software whilst pressing Alt-Ctrl-Shift as soon as you click the icon to open it. It will then open a dialog to give you the choice of starting with the defaults it had when it was first installed.
Make sure you explore the other options first as you may not want to have to start setting up Illustrator from scratch.
You need to use the '3' key on the numeric keypad of your keyboard, not the row of number keys just above (on a US keyboard) QWERTY.