In your Admin, under Customers->Orders, you say you can see the orders, right?
In the column labelled "Payment/Shipping", there are some codes related to each order. What are the codes next to these orders for which you're not getting any money deposited?

If it says "cc" then ... the orders were placed with the offline CC module, and thus you'll have to process those cards manually ... the website didn't charge the card, because it can't do that with that module.