I too can't imagine having/operating with more than one computer, or not having one "at hand" at virtually all times, and would urge you to get a laptop. I think you'd find it worth the personal expense if your company or university doesn't pay for it, more than worth it, actually, more like worth its weight in gold since if you're working with GTD you must be inherently organised (or trying to be, like the rest of us seem to be also!).
Given a single laptop, I'm (newbie) working with a pretty basic GTD approach. I don't have a palm device (hangs head) and use a combination of simple Word document (3-pages holding all lists) and daily paper calendar on which I put the 'usual' hard meetings, calls, and commitments and various little post-it notes of quickie to-do's as I think of them. My company calendar system is Lotus Notes (I never copied all my work calls and meetings onto paper - just used Notes) but I am leaving the corporate rat race so will use the combination of Word and daily paper calendar going forward.
From your original post I would think the single most helpful thing you could do for yourself would be to start with "one computer, one life" and go from there ... good luck to all of us.