Battery confusion

I was planning on using this http://www.ebay.com/itm/1-PCM-Prote...647?pt=LH_DefaultDomain_0&hash=item3372a94f77 as my 14.8v protection circuit for my gamecube portable. The problem is I have 8 3.7v 1200mah lithium ion cells that I harvested from a laptop battery. I was thinking if I could wire the cells like this:
Make 2 cell packs with each in parallell for a total of 4 3.7v 2400 mah packs and then wire them in series using the protection circuit for a 14.8v battery pack with 2400 mah.
If I can do this, how long would the gamecube battery survive? Also there was a pcb inside the laptop battery pack that seemed like a protection circuit but I am too skeptical to try and use it because the circuit may be inside the laptop itself. If i could use that pcb it would save a lot of time and hassle.
Thanks in advance
 
That would work. The description has the wiring instructions, just treat every parallel cell pair like one cell. Not sure how long it would last, probably 1-2 hours, with 2 being very surprising. How old are the cells? They lose capacity with time and use.
 
Thanks again for responding. The cells are pretty old, so my battery life prospects aren't looking very well. However, the only reason I have the batteries in is so that I can show it off that it can run without plugging it in. At least, for now I'm going with this. If I can find other batteries that can give me good results for cheap I'd go for it.
 
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