10 years? 10 years is a loooooooong time. No, it won't. In fact, odds are it won't be running after 10 years, statistically speaking, without some kind of part replacement.

At any rate, 4GB of RAM won't last that long to keep up with modern games - but RAM is very easy to expand later, so it isn't really that big a concern. The video card won't keep up, either, over the long haul (and won't run some current games very smoothly already).