Duke, Welcome to Sevenforums!
Likely it has something to do with the Dell hardware that causes this issue. My guess is if they don't know how to fix one of their own computers (or they know that it can't be fixed), then I am not sure if someone else would.
Generally speaking, sleep mode and connecting to the internet isn't effected by the amount of RAM one has (to my knowledge). But I do not know if that is true for Dell computers or select Dell computers. I myself own a computer with 12GB RAM and have no problems. I used to own another computer with Vista, and I managed to have sleep mode working perfectly, but on certain installs, the internet wouldn't work after a wake from sleep mode unless I restarted or disabled/re-enabled the wireless network device. My guess is it would be hardware related. Try updating everything in windows update and download all recent drivers. If you need help on the driver side, please follow this link: New to SevenForums? Fill out your system specs (this tool may help you out a great deal).