Which browser are you using, and are you using Adblock?
Looking at your GPUs very low specs, this would bottleneck your system in things like games but shouldn't really harm browsing. It appears that the Phenom CPU may also be a factor behind slow speeds, but this would be noticeable through the entire system.
I recommend switching to Opera and enabling its built in Adblocking tool from the browser settings (Found under the browser logo in the top left hand corner). This should reduce the workload on your CPU. From the same menu you can also access "Opera Turbo", which may increase speeds if it is your raw internet connection to blame, rather than your PC.
You can also try taking checks on Speedtest.net on your wifi with that pc and another device, if the results are the same, it is your ISP that is to blame - and it may be worth looking at different ISPs in your area with faster speeds.