Check your policy! If you've got new for old cover (not indemnity) and accidental damage, and the value of the laptop did not exceed the limit for individual items, then you should be covered. I'm assuming that your friend can verify the sale and that you still have the broken lappie (for inspection/salvage)
As far as making a profit, you are only asking for a comparable replacement - the fact that you bought the laptop at a bargain price shouldn't make a difference. As an example, if you bought a colour tv in a sale and you dropped it, would you accept the value of a black and white tv from your insurer as a replacement? Hope that makes sense! And good luck!