@jaybarbara, if the power LED goes out, the router may not be able to retain it. I would suggest that you try plugging the router to another power outlet or use another power adapter like what bigdave suggested. This will help isolate the issue. Here are the specs:
You can also connect your computer to the router, open command prompt and check the router's IP Address. You can follow the procedures on this link: http://kb.linksys.com/Linksys/ukp.aspx?vw=1&docid=4a3527c394744e7ba4a433c3499ecc85_Checking_the_Router_s_IP_Address_when_Using_Windows_7.xml&pid=80&respid=0&snid=2&dispid=0&cpage=search