Ummm....unless that laptop was specifically packed with hardware geared for gaming, more than likely it won't be good for anything other than daily routine things like web-browsing, Microsoft Office applications, watching videos, etc...So the very big question is what's the hardware inside this notebook???? Or what's the specific brand and model of the notebook??? With that information, we can tell you how well it will game....if it can game at all.
The other question is what games you're trying to run?
Games don't specifically mess up laptops, but it certainly can cause them to overheat if we're talking about the notebook having a dedicated video card playing an intensive game and you have no adequate cooling for the notebook. If the notebook comes with a garbage onboard Intel Integrated Graphics Chipset (not a real card), then most modern games will simply not run (crash) or run on VERY low settings if lucky.
The gaming on a notebook vs gaming on a desktop question is too open-ended and is hardware dependent. But the reality is you will get more in terms of hardware performance in a desktop than you would a notebook of the same price assuming you shop right, which most people don't do. That's why there are threads like this one to help people out.
I can't find the exact model, but it's a toshiba and it's either one of these two.
http://www.bestbuy.com/site/Toshiba+-+Satellite+Laptop+/+AMD+Athlon%26%23153%3B+II+Processor+/+15.6%22+Display+/+3GB+Memory+/+320GB+Hard+Drive+-+Helios+Black/9992957.p?id=1218206200932&skuId=9992957
http://www.bestbuy.com/site/Toshiba+-+Satellite+Laptop+with+AMD+Turion%26%23153%3B+II+Dual-Core+Mobile+Processor+-+Midnight+Breeze/9705346.p?id=1218154375878&skuId=9705346
I plan on playing games like CoD4, maybe counter strike, LOTR: Battle For Middle Earth 2, and some Age of Empires games. but not anything like starcraft: wings of liberty or crysis.
If I were to just build a desktop and play games like this, how much would it cost? (I currently have 170$ saved up(which I know isn't enough) but I'll keep saving up until I have enough, and I'll get some money at christmas)
Thanks for all the help by the way.