A router is a network device...it is totally unrelated to the hard drive (I'm assuming you're referring to an external hard drive and not the computer tower). At any rate, you might google "wireless router image" so you get an idea of what one looks like. Generally, on the back of wireless routers, there are also network jacks (it doubles as a wired router as well). Network jacks look like phone jacks, only bigger. If you have 2 computers that both access the Internet, then you most likely have at least a wired router. If there is an antenna on the router, then it is wireless as well. There would be a wire going from your cable or dsl modem to your router, and then potentially wires going from the router to your 2 computers. Or more likely, you have a wireless router and have wireless network cards in each computer which communicate with the router wirelessly. Laptops these days come with wireless network cards built in. Desktop computers sometimes have them.
Long story short, if you verify that you have a router, and if it is wireless, you could buy either a wired or wireless IP camera. If, however, your router is only wired, then you will need to buy a wired IP camera. IP cameras will communicate directly with your router...not your computer initially. Your computer (including the icamsource) can access your IP camera(s) through the router.
If this doesn't help, locating the brand/model number of all equipment hooked up to your cable/dsl router...or try taking some pictures of your cable/dsl modem and all equipment hooked up to it, as well as the back of the computers. Maybe someone can help tell you what you have.