Well, my problem may not be the same problem some of you other guys are having.
I have a flash cart that only works in some of my consoles (others it will boot to the blue menu screen, but hang when you try to start a game). The flash cart uses more power than a normal cart and we determined the power supplied by these other systems just wasn't enough to run the bank switching.
For example: it works 100% fine in the Duo and in a GT (JP TurboExpress) when powered using the AC adapter.
It will not work in a TG-16 core at all, or the GT when powered by batteries.
I found out after testing that the folks that sell these didn't actually have access to a TG-16 or TG-CD deck for testing, only PCEs and Duos. Which explains why many people report problems with the carts when trying to run them with a TG-16 core.
Overall, I'm still happy with my purchase because the cart is technically just fine, and I can play it flawlessly in my Duo 100% of the time. I just can't use it in my bedroom where the TG-16 core is.
However, if this cart you've got isn't powering up at all, on any system, anytime, it sounds like it's fried.