I thought I'd be in that position too, but unexpectedly got the money to replace my old dinosaur of a computer last summer; that old computer was so old it was beginning to have sentimental value. Originally built it from components in either late 2004 or early 2005, can't remember, I'd upgraded it gradually replacing all the parts, so that in the end only the motherboard and the case were the original parts.
When I originally bought it, I opted for an AMD motherboard with socket 939, which was newest thing then, just so that I could keep upgrading as long as possible, to keep it serviceable and running the games I wanted to play. Worked for nearly 10 years. In the end, it could run all the new bioware games, and mostly with better than the lowest graphics settings too, but DA:I would have been too much for it, and because of the old socket 939 for which no new processors were being developed, and the fact that it only had an AGP graphics slot, it had come to the end of it's upgrading possibilities. Every component was already pretty much the best that was available for that motherboard.
The funny thing was that when I replaced the computer for a new one, the next electricity bill I got showed that I'd experienced a 29% reduction in my apartment's electricity usage. Apparently my old dinosaur was a bit of a power hog. 