Formula to refer to array in another sheet that shifts based on date

Hi guys. I'm currently trying to build a formula that takes a list of quarterly electricity prices, quarterly dates, a quarterly electricity consumption figure, and a consumer start date to calculate an overall power cost for different consumers. The formula will be placed in sheet one with the consumption figure and start date, while the prices and quarterly dates are in sheet two.

The formula should multiply the consumption by each quarterly unit price in the array that have an associated date occurring after the start date (in this case I2 onwards), and summed. In this case this adds up to $4610. Of course if the start date was for instance, 1/1/13, then the array would consist of I8 onwards. I thought I could do this with an index/match but got stuck trying to work out the logic for changing the range based on the start date. If anyone has any input that would be greatly appreciated. Example sheet is attached, hopefully I've explained myself clearly, let me know if not. Cheers in advanceExample.xlsx.