I ordered a laptop by invoice but didn't get an email. Nothing is displayed in "My Orders" either. I've tried again but it doesn't work.
The payment on account was probably declined by Amazon. You can check this by changing the filter to "canceled orders" under "my orders".
If this is the case, your order, which has since been canceled, should be displayed there. In this case, payment is only possible by credit card or financing in cooperation with Barclaycard.