To help you out I would need a little more info like, what OS's are you running on the system? What Liksys router do you have? Is the Linksys directly connected to the desktop computer? Has it ever worked or are you just now having this problem? Does the connection on your desktop work on any other website (The ones that don't require secure login) or are you unable to connect to the internet all together?
Correct me if I'm wrong but from what it seems, your internet connection is working fine, except the desktop computer cant access secure sites. If this is the case chances are, that the router isn't whats giving you trouble. I found a post that might fix your problem, so go ahead and :
Take a look at this forum.