You did not say what mac or os you are using, so it makes it a bit harder to nail down the problem. However there are options out there on a tight budget for a student to fit the bill. If you are running 10.4.11 or better you are much better off. OpenOffice is available though you will have to...
Thought I would drop a quick reply here. I think you are on the right track with the system board. That model of G5 has had a bad rep with all sorts of hardware failures:
http://lowendmac.com/ppc/power-macintosh-g5-2004.html
The upside? I have seen replacement boards on eBay for a nominal...