Sorry it took so long to reply, for whatever reason Yahoo sent the reply notification email to my spam folder, so I didn't see it.
This is what I understand so far, I hope I've got it right:
You want to change cases and power supplies. You can't put your OEM board into a new case, so it's either buy a board with the same socket and use the current CPU, or change motherboards and get an i3-6100 and an 1151 motherboard.
There are a couple things you should consider here.
-If you plan on using the same memory, you need to make sure the motherboard that combo comes with supports it. There are 1151 boards that take DDR3, DDR3L, and DDR4 memory. Your system either has DDR3 or DDR3L. You also run the risk of that OEM memory not liking the new motherboard, it does happen from time to time. Memory is not my strong area so I can't advise you on that.
-Changing CPUs is a double-edged sword. On one hand, the i5-2400 isn't a slouch just yet. It's still a very capable chip. You could get by for another few years with it. And by changing to the i3, you would be losing two physical cores. On the other hand, however, changing to an 1151 motherboard is a good idea because it opens up a very nice upgrade path; supposedly Intel's next line of processors, code-named "Kaby Lake", will fit in the 1151 socket. So if you decide to upgrade the CPU in the future it will be very easy.
If you change out motherboards, the end result will basically be a newly-built system, save the memory and any hard drives (assuming you plan on re-using/can reuse those). Keep in mind that you will need to acquire a new copy of Windows since the current installation will no doubt detect the change in motherboards...
If you want my personal opinion, I would go ahead and spring on that combo. Assuming the motherboard that's included in it isn't garbage, $190 is a pretty good price for both components. You could sell the i5-2400. Or maybe save it for another build - I think I could make a nice ITX build with one, for example.
Whew. Sorry for the long post.