Defective Brand New Laptop. Dell refusing return

I bought a New Vostro 3520 from Dell.com and from the get-go, the laptop has been shutting down to "recover" once every 3 hours. Contacted support to return the clearly defective laptop (It had been 6 days). They made me do diagnostic tests and reinstall the OS. The next day, the same problem happened only this time there was a screeching sound accompanying the shutdowns. I kept contacting customer support and they either kept switching me from department to department or plain cut my call. The last time I called they said because I have basic warranty, I can't return the laptop. The laptop keeps having the same problem without a solution. I just want to return the laptop and stop this business.