Well, I think it depends on what you mean by "blown". Blown up? Overheated and expanded? Or just no longer functioning good, with no visible signs of any damage?
Any of those can indeed cause this situation. To test, you need a known good identical battery to try in your BB. Likewise, an identical BB without problems, to use your current battery in. The results of this test will indicate if the problem indeed is your battery, or something else about your device itself.
Good luck and let us know!
Occam's Razor nearly always applies when troubleshooting technology issues!
If anyone has been helpful to you, please show your appreciation by clicking the button inside of their post. Please click here and read, along with the threads to which it links, for helpful information to guide you as you proceed. I always recommend that you treat your BlackBerry like any other computing device, including using a regular backup schedule...click here for an article with instructions.