Are you still working from a factory install, or an in-place Upgrade to Windows 7 from Vista? How was Windows 7 applied to new HD? You really need a clean install to wiped HD to know it's not OS.
Test your RAM with memtest86 for 5-6 passes or overnight to really stress test it. Swap and reseat RAM sticks. Swap out cables to make sure they're good.
Study the Event Viewer>Admin view to google repeat errors to find how others have resolved them. Do the same within Performance Log on Advanced Tools page accessed by clicking WEI score at Computer>Properties. Check also for cued issues at top of Tools page, then Generate a System Health report there.
Compare the drivers
offered on the maker's Suppport Downloads webpage with those in Device Manager to try newer or different drivers - you can always roll back on Driver
Continue troubleshooting with Tech Support as you want to benefit from parts replacements to have it sorted well before warranty expires.