What version of the webphone plugin are you running (displayed on the sample page) ?
As a first test, could you try to click Login after entering your username (wooitan) and CUCM address only (no password), leaving mode to SoftPhone and "Server Auth" unchecked ? The sample application should register straight away (unauthenticated) and the Make Call should become enabled.

Can you see any error in the logs ? File path is
XP: C:\Documents And Settings\{user}\Local Settings\Application Data\softphone.log
Vista, 7: C:\Users\{user}\AppData\Local\softphone.log
Mac: /Users/{user}/Library/Application Support/softphone.log
where {user} is the Windows or Mac user id