The problem with mid-range and below PCs is that most manufacturers build them to run 'as is'. Thus they give it 'just the amount of power that it needs' and no more.
I had the same situation several years ago with a Dell computer that had a 200 Watt Power Supply. I spent a lot of time, research, and money trying to find a better card that would work. I got an ATI 9250 which I think was rated at 250W. The results were no appreciable improvement over my Nvidia MX400 and that the computer would shutdown and reboot when the card was under load because it was under-powered.
It is sometimes hard to upgrade pre-built computers for this reason alone. Not to mention some have custom connectors which cause some comparability problems.
After realizing this I spent the next 6 months saving up money to build my own PC. When I was done I was so glad I did because the results were fantastic.