System details = First time LW user, it won't connect
I believe your Linksys device is the issue. That model Linksys is a bit of a lemon; it's an infamous model. It is unreliable & has major firmware issues. WRT54G to fix these issues (1) Port forwarding is a quick fix. Though still may show some occasional drop in connection from time to time. (2) Make changes to firmware yourself (if you have doubts, don't do it.) You can find a post refering to this model under Linksys & under the UPnP section of this post: Connection problems? Check here first! (click on link) & look for WRT54G

Can you still use LW with the firewall issue? Yes. Will it affects its abilities? Yes. What it will do is make it more difficult to connect to extra sources. You will never be able to become an ultrapeer. You will never be able to direct connect to a friend. People will greatly struggle to upload from you. Not having uploaders means less sources you are connected to, thus reducing your search & download results.