Can I install it on my new computer after it's already been installed in my old one?
If you do not plan on using the old computer, you are better off deactivating your suite, then uninstall. But as far as the license goes you are allowed to have it installed on two computers but only one copy can run at a time. This is meant to allow you to have it on your desktop and laptop as that is the most common senerio.
If you already have it installed on two systems and can not access one of them to deactivate it, you can call adobe and see if they can do it for you, not sure if they will but it is worth a try.