First thing to do if running it without a fan is to either get another (spare) graphics card and put that in for the moment. If that is not an option, try to underclock the Geforce chip (and memory also if you want as this generates heat) as much as possible, but I have a feeing that will not be enough.
Running without the case on will not actually do much for you. Also try to elaborate on how you 'cut the fan out'. Do you mean that you cut the fan on the card off from the heatsink?
Either way, you will have to probably remove that old heatsink to get a proper replacement heatsink and fan. Also, if the card was still in warranty, you could have probably got a replacement unit, but I think cutting things out has now voided that.
As to replacing the heatsink and fan yourself, I cant really say much on that as I haven't done much to graphics cards, but by searching around you should be able to find some information on how is best to do this.