I placed an order for a laptop, with additions, on 30th December with Dell. I did it on-line but then placed it over the phone. I also applied for 12 months interest free credit.
I've just checked on-line and it is in transit to me, I phoned the carriers and it should be delivered on Wednesday.
So it would seem clear that there is a major problem with your daughter's order. The first order number I got was a 'booking number' not an order number, but Dell later gave me an order number.
I'm not surprised your upset, they really should keep you informed.