Re: Blackberry curve 8530 (sprint) radio off??
Sounds like a hardware issue of some kind. The easiest thing to try would be placing a paper shim along the edge of the battery opposite the side with the electrical contacts. Just a single strip of a business card or notecard should be enough. If the battery doesn't fit snugly, the slightest disruption of power can cause things like the radio to turn off without shutting down the entire BlackBerry. If the battery got hot during charging even once it's possible it deformed slightly with that excess heat. Afterwards it might not fit the way it used to fit. Anyway, it's a quick and free thing to try before buying a new battery.
Consider borrowing a battery from a Sprint store and using it for 5 or 10 minutes in the store, just to check the battery idea before buying a new one. And if/when you do replace your battery, get a real OEM BlackBerry battery, not a cheap eBay knock-off.