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I'm sorry, but this is a terribly dangerous idea. I'd consider myself some-what of an expert on the Li-ion chemistry.
First off, I've cracked open a number of laptop packs and analyzed them on my Computerized Battery Analyzer. Almost all cells from packs that I've skavenged have been complete junk. Huge increase in internal resistance, and huge decrease in capacity. Many only delivered 25-50% their rated capacity at 1C.
Secondly, Lithium Cobalt cells are only designed to safely deliver currents of up to 2C discharge. I'm guessing that these cells would provide about 25% of their rated capacity at this type of discharge current. It looks like your running maybe a 4s4p configuration. With a car you could very easily try to draw too much current.
Thirdly, Lithium Cobalt cells must be balanced. Each cell must be matched with other cells of similar internal resistance and capacity. I see that you are using at least 2 different types / brands or capacities of 18650 cells in your pack. This is EXTREMELY dangerous, especially for older cells.
If there was a catastrophic failure of this pack, it could be fatal (and no, I'm not joking). I've read stories and seen pictures of people who had un-matched 18650 cells explode. One guy almost lost a finger.
I would urge you for your own safety and for the safety of your car, to abandon this project immediately! This looks like a huge disaster waiting to happen.
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