It would fit in your case fine. Your 300w PSU would be close with a 100w TDP 550ti. And your PSU probably does not have a spare 6-pin PCIe cable.
Anyway, the Pentium Dual Core will most likely be a bottleneck for many games and you can't overclock. 550ti isn't a high end card but it would be bottlenecked, but it would be better than your HD 4650. You could buy a new PSU and GPU, but you'd be dissapointed in your CPU.
This card isn't quite as good as the 550ti but it uses half the power and doesn't require a 6-pin. You'll still run into issues with your CPU in most games though: http://www.newegg.com/Product/Product.aspx?Item=N82E16814102969
I'd recommend getting a new computer (or building one!!
) If you don't want to get a new one or can't afford it, the HD 7750 is your best option for improvement.
Edit: CPU bottleneck depends on what games you play, BTW.