Inspiron 15R SE7520 2 weeks old and crashing

I received my laptop 2 weeks ago today and since that time it has crashed at least 10 times. When I say crashed it has done a variety of things: the screen has gone black, it has beeped, sometimes 4 beeps, sometimes 1 beep (both repeatedly), the screen has been covered with odd symbols. Sometimes I've been able to restart it simply by turning it off and then back on. On one occasion it took 2 hours to restart and this morning it has just turned itself repeatedly despite it doing 2 system restores and I have given up. At varying times during my struggles this morning the following were displayed on the screen:

I had originally asked whether anyone could advise what steps I should take to return the machine but as I have had no answer I wonder if I could ask for other suggestions. I need to have access to a computer daily and thank goodness I still have my old desktop which hasn't quite given up the ghost but it is on its last legs and I am pretty desperate to get the Dell situation sorted out. I should mention, in case it's not obvious that I have extremely limited computer knowledge!

Thanks (in hope!)