The 1402 Office error is a problem that's caused when you try and install the Office package of applications to your computer. It's specifically caused by your computer's inability to access a certain "registry key" on your system, preventing it from being able to install the files & settings that are required.
This error will normally appear in this format:
Error 1402. Could Not Open Key
The specifics of this error are quite precise - in that it will be caused by your computer's inability to place certain settings into the registry of your system. The registry is a huge database that Windows uses to store vital files & settings for your PC, and is where everything from your desktop shortcuts to your software's options are stored. Because Office is such a complicated program, it has many registry keys it need to insert into this database… and the 1402 shows that this cannot be done.
There are generally two reasons why the 1402 error will show - the first is that you're trying to install the Microsoft Office software onto a PC that doesn't have a registry database (versions of Windows prior to '98 don't have a registry), and the second reason is that your user account does not have the correct privileges to install programs on your system.
The way to fix this problem is to initially ensure that your computer is able to actually install a program like this - if you have Windows 98 or below, then you really need to upgrade your system before attempting to install the likes of Microsoft Office. If you have a compatible version of Windows, then you need to look at changing / updating your user profile to ensure that you have enough permission to install the programs / files / settings that you need on your PC. It's also recommended that you clean out the "registry" of your system with a registry cleaner - which should remove any potentially conflicting files / programs from your system.