I finally figured it out, and I feel like a dumb@*&
I finally figured out that the spring contact on the bottom of the battery compartment was too wide, and not touching the "button" on the top of the rechargable battery's (where-as the Alky cells have an all metal top on them, so it didn't matter where the spring hit). I just took some needle nose, and gently crimped the top ring of the springs to that it would touch the button. I can now use either rechargable's OR alky cells in my lights!!!
Pelican did advise me that they feel the rated burn time on the bulb would be reduced by 50% due to "the higher power that rechargables put out", so as a precaution I purchased a few extra bulbs. They weight a whole lot less than an extra set of 8x C cells!
BTW, I should also mention that I did purchase 2 of the PT Shockwave LED lights, but one arrived broken so I sent it back. I went ahead and kept the other, figuring that some fateful day I'll break or flood one of the Pelican's...
So, if anyone had been following along, just make sure your batteries are making contact (metal to metal), I didn't even think of that till sitting and staring at the lights for about an hour....
PS The C Cell rechargables that I got, have a plastic coating on the + side and only the "button" on top is metal, where-as with other batteries the entire top is metal.