You can edit text files (not Microsoft stuff, just text) with vi, vim or emacs. You can connect to the web with lynx. The others, well, I dunno -- there might be but I'm unaware of them.
Pretty much any distribution can be used in text-only mode; I can recommend Slackware because you "install all" and you've got pretty much everything you'd want. Slackware doesn't do a lot of things "for" (read that: to) you so you configure it the way you want it to behave. That means a learning curve but the rewards are directly proportional to what you put in; i.e., you'll wind up knowing what you're doing. Other distributions I'm aware of start out graphic and tend to want to stay that way but certainly can be run in non-graphic mode.
Something to bear in mind is that Linux is not Windows (or, for that matter, Macintosh); it's far more efficient that either of those and running KDE or one of the other window managers that come with distributions is vastly more satisfying than screwing around with XP or, shudder, Vista -- you don't deal with weekly security updates and things run fast and smoothly.
Hope this helps some.