I'm trying to draw 500 samples from a population of 10,11,12,13,14, and 15. Each sample will be n=10. That's the easy part. Now I can't figure out how to produce the R-code to calculate 500 separate Confidence Intervals (CI) using a student's T-test. I have tried everything, but apparently there is a way to do this. Following that, I need to calculate the actual number (proportion) of these CIs that contain the "true value" and compare that to the anticipated number (i.e. a 95% CI would mean that 95 out of 100 samples would contain the true value). Any help would be great, thanks.

I think you are probably looking for the apply function as in the attached R Script.

May be you can see boot{boot}, there are standard bootstrap methods.
Please read the example in help pages, and then you can deal with you problem by yourself.