If you don't have anything you need to save on this system yet - I would install fresh and do all the updates at one time.. just in case that is part of the problem.

Do you have the key code with the disk you have?
It will be registered to the other computer, but if you aren't going to use that old one anymore it should be fine to transfer to this newer one.

It isn't that hard to install, but is someone nearby you could call if you have ea question? Basically it asks a few questions and you click the answer and the rest is automatic for the most part..then type in the key code to authorize it.. I'm assuming it is pretty much like installing XP or any other operating system.

A dirty mouse ball or optic will cause some jumping and odd stuff.
So a wipe down might be a good 1st choice.
The typing issues might be dirty keyboard ...
there are you tube videos on how to clean those.

The hardware issue is so hard to pin down for sure...