You mean physically as in enough uh, thingies to plug it into or as in effs up the system somehow internally with too much RAM? How would I check this?
Could be both, but it won't hurt your system. You would just need to go back to the smaller amount. The main issue is that a computer of that age might not recognize a larger amount of RAM, even if the modules fit in the slots. I would go to Dell's support page, and enter the service tag number. It will be on a sticker somewhere on the back, top or side of the case, and it will be something like 812BX4G. Also, go to New Egg or Crucial Memory, and ask their memory configurator what sort of RAM your model of computer will accept.
There really isn't a downside to trying out Microsoft Security Essentials (unless you're worried about the personal information issue that someone mentioned). MSE is free, and if it slows things down, try something else. Just make sure you have some other Anti-Spyware in mind, as a back-up.
As others have said, MSE is very light on resources. However, comma, even though it doesn't slow my computer down during start-up or normal operation, it does take an extremely long time to actually complete a full scan. Even so, I have other, slower computers that don't have that problem at all.
Also, if you use Spybot, and it slows everything down to a crawl, disable Tea Timer. In fact, there should be an option whether to install Tea Timer, when you are installing the rest of Spybot. Check no.