You can have 5 computers/devices undert the same itunes account.
Have you signed in to itunes on the new computer and authorised it? (Look in the itunes menus and you should find these options).
Once authorised you can then download your past purchases.
There is a share library option - never used it myself, so not sure if you could pull the cds that you have manually added onto the laptop across to the new pc.
If you have a big enought usb drive or an external hard disk you can copy the files across that way - Apple giv instructions on how to move your itunes library from one comouter to another - that would work and then you'd have the music on both computers.