In my opinion doing an overhaul on a computer like that just isn't worth it. A single component I would probably do. For $350 you can buy a low end Dell and you can
build your own for $300 or possibly less. I would ask for an advance on your money or try to eek out a little more time on what you have if you can't scrape together the money yet.
Oh yeah, and $200 a month? I was happy if I got $5 a week from my parents when I was younger...