I don't know anything about networking, and I have a wireless router, but I only use it to connect PCs with wire. My concern is wireless may not be secure. My question is: if I turn on wireless and somebody gets into my router through wireless, can they get into my desktop wired to router?
Potentially, yes. If you have not done anything to your router other than to plug it into the internet and an outlet, it may be unsecured. Depending on the router, you may have the options of either a) securing the wireless or b) turning off the wireless completely.
Wireless is awesome when you use it, but to leave it on, unused, and unsecured is not the wisest thing to do.