CPU usage can be checked through the task manager readily enough, as can memory usage. At 800x600 resolution, memory almost certainly isn't the problem however (unless you have an abnormal number of programs running in the background).
That said, your system more than meets the minimum system requirements for the game, so your problem may be elsewhere.
Generally speaking, choppy video can be the result of any number of things:
Lag - slower interent connections will cause problems in most games these days. Often, while your system waits for an update from the server you don't get a new frame of animation. Generally this is the result of packet loss more than actual latency howver. Cellular internet in particular is terrible for many online games for this very reason.
CPU - While most of the graphics processing is done on the video card, the core game code is being processed on this device. If the system is struggling with the execution of the game logic, you'll have problems regardless of the video card. Generally, a frame is produced for each pass through the game logic, and most games only have one frame in the buffer, so problems are rapidly seen. There can be a number of reasons for this - lack of power on the CPU is the most obvious. Hardware settings may be at fault (though I don't believe CS:Source has an option to use anything other than hardware accelleration for video, I don't want to download it again to check). In some cases, heat buildup is the problem. Many CPUs clock themselves down if they reach dangerous operating temperatures. The most common cause for this is dust build-up on the CPUs heat-sink or the failure of the attached fan (or case fans)
Video - In this case video is the last culprit in the list simply because the card exceeds the requirements by a significant margin.
