|If your computer doesn't have wireless connection to the router, you'll need to plug in an Ethernet cord from the router to your computer for a wired approach, or use a computer that is already connected wired/wireless to the router.|
Once you have that physical connection, you can try going to your router's admin page. This is usually 192.168.1.1 but not always. To find out yours, open up Command Prompt (Start > Run > type: cmd) and type in ipconfig One of the results will be Default Gateway and the IP address for it is your router's admin page.
Once you're in the router's admin page, direct yourself to the Basic Wireless Settings page (or something named similar) and check the Network Name (SSID).
Edit: Terii beat me to it.
Apologies if I don't respond to your reply immediately. I don't check this site daily, but you're welcome to PM me as a reminder.