In WinXP or in Vista, the "shortcut" to turn on "Sticky Keys" is to press the space bar five times in succession.
This makes it quite easy to accidentally turn on this "Ease of Access" function inadvertently, if the function has been enabled (which can sometimes also be done accidentally).
You should get a popup asking if you intended to turn on this function, but it can be easy to miss, since the popup usually disappears if you hit a next (sixth) consecutive space.
This function allows you to enter multi-key inputs, such as Ctl-Alt-Del, one key at a time. If it's turned on, the computer may think you're entering a multi-key "command" and will "lock up" until you enter a second key that is part of a command that it recognizes and can execute. If you enter a repeat of the same key (which is not usually a continuation of a shortcut combination) the computer may get confused and just sit there and stare back at you.
In Control Panel, you should find instructions/explanations in "Ease of Access Settings" or "Accessibility Options," depending on which version of Windows you're using.
There are a couple of other similar functions in these groups that can make weird noises and/or require different handling of your keyboard inputs; but the Sticky Keys is the most likely to cause what you've described - if it's a "normal" Windows function.
Of course, as has been suggested, it could be just a bad keyboard.
If, by chance, it's a wireless keyboard, checking/replacing the battery(s) might be in order.