There's your problem
Intel i3 M350 (First Gen)
HD Graphics 1696 MB (again, First Gen)
Forget the internet, start an offline game with/without bots (you don't need the bots for this) See if it lags there as well ... Type in net_graph 1 in the console to see your FPS in the game (works off and online, not cheating) If you are lagging when playing offline, then it's not the internet that's at fault.
Please note that it MAY not lag AS MUCH as it does when online, to stress the game, add bots, throw some smokes, if it's smooth and you get goof FPS then it's the internet, if not, it's the machine that requires upgrade.
If it is in fact the internet, there are few things you can do to help yourself:
- Make sure you are not torenting. Seeding especially, hurts the internet ALOT, so shut down any torrenting clients.
- Shut down any software you don't need, especially the browser. When I decided It's time to play CS i shut my browser, I also have Team Viewer, and some other programs I'm using. I switch everything off, except Steam ...
To clarify on my first lines: I know that on paper the CPU and the GPU might be good "oh look it has 2GB of video memory although CS requires only 128mb" etc etc ... I KNOW but not many people realize how bad the Integrated graphics really are, and how much worse the Gen 1 are ....
EDIT: To be honest though Windows 8 and 8.1 are quite optimized for old systems, and the RAM should be more than enough. But as mentioned I strongly believe it's the CPU and GPU that bottlenecks and not the internet.
EDIT2: SpeedTest Latency is different than the one in CS, but 50 is quite fine for multiplayer.