Windows 7 Still active if I move my Hard Drive to a new computer

Since most computers come with Windows, if you are using your current Windows 7 for the new computer - does this mean you're building your own custom computer? If so you need a Full version license of Windows 7, not an upgrade.

Can You Move Windows 7 To A New Computer 

If it's a retail Full or Upgrade license - yes. You can move it to a different computer as long as it's only installed on one computer at a time (and if it's a Windows 7 Upgrade version the new computer must have it's own qualifying XP/Vista license). The previous Windows 7 installation on the old computer must be formatted/deleted. You might have to call Microsoft and explain what happened to complete the activation. Activating it on the second computer will automatically in effect "deactivate" the license for the first computer. The key will work with both 32 and 64 bit, but only one can be installed at a time.

If it's an OEM license - no. OEM licenses, including Windows preinstalled on a computer before purchase and Windows bought separately, are tied to the first computer they are installed on and can not be transferred to a different computer. To install Windows on a different computer you will need to buy another copy.

If online activation fails:

Call Microsoft Using Manual Phone Activation

If you have trouble activating Windows 7 you can call Microsoft to activate by doing the following:

1. With Windows running click Start, then in the Search box type:  slui.exe 4

2. Press Enter on your Keyboard

3. Select your Country.

4. Select the Phone Activation option, then call the number given and hold for a real person.

For more details:

http://www.sevenforums.com/tutorials/18715-activate-windows-7-phone.html

Note: If it’s an Upgrade - if you are still installing Windows and at the Enter Your Product Key page, do not enter your key and uncheck "Automatically Activate When Online" then click OK/Next to finish the installation.