The obvious question is - have you already asked Giganews tech support for help? Also, have you changed anything lately, such as installing software, changing settings, or whatever?
You don't say if you use a router, or what your ISP is. Those are potential (but unlikely) problem sources. Have you enabled and looked at Newsleecher's log file? **Can you copy and post it here?** Do you have an antivirus installed? a 3rd-party firewall? Windows firewall enabled? Can you ping Giganews server?
Your basic end-to-end 'routing' goes something like this:
Newsleecher --> (antivirus) --> (firewall) --> PC connection ----> (router) ----> ISP -----------> Giganews
So there is obviously a failure/blockage at one of these approximately 7 possible points along the way
Just using basic logic, I would try eliminating non-essential services and substituting the essentials, and narrow down the problem by the process of elimination.
I would do the easy stuff first: connect to a different Giganews server and change the port.
Then I'd (temporarily - for testing purposes) turn off the antivirus and if that doesn't help, disable any 3rd-party firewall.
In case the problem lies with Newsleecher, there many other newsreaders available to try out, a lot are free.
To see if the problem is at Giganews end, there are many free usenet providers to try out, (many with binaries) Here's two that offer easy (no credit card) trials.
http://just4today.net/
http://www.hitnews.eu/
If using a different usenet provider as well as a different newsreader - as well as eliminating the possibility of the problem originating with the AV/FW/etc, and it still fails to connect, then what could have been missed?