Netscape 4 is an older browser and it doesn't understand more recently adopted style rules -- such as border-left-width:0 and so on -- rules which more recent versions of FP may write into your code. But Netscape 4 does understand <table border="1">
Since all those other style rules are not understood, then all Netscape knows to do is give you a 1 pixel border! Try setting all your tables to border="0" where you don't want to see any lines. That's the most straight-forward way to deal with this issue.
I'm going to move this thread over to our WYSIWYG Forum where the Front Page people hang out. You'll stand a better chance of getting the help you need configuring FrontPage there.
Just one more comment -- even though WYSIWYG editors invite you to think about HTML as if it was a layout program, it isn't a layout program. So making changes in a WYSIWYG editor just on the basis of getting the "look" you want can lead to some nasty surprises in other browsers (as you just discovered.)
You definitely can create good sites in FrontPage and other editors, but it still takes some decent knowledge of HTML and CSS to really get it right.