Iphone Battery – Software Issue?

I had a jailbroken/unlocked iPhone which, all of a sudden (after using a emergency battery backup device) began running extremely hot, and drained the battery from 85% to 0% within an hour. since then It would not turn back on, react to a charge, plugin to iTunes, or a DFU reset attempt.
I ordered a replacement battery from direcfix.com (great resource for replacement phone parts!), replaced it, and it powered back up, but only at its 4% charge, and would barely even hold that when plugged in, it eventually ran very hot and drained itself back down to oblivion.
I am certainly not blaming the battery, I am just asking if anyone has heard of this before and if there is something I can replace that is cost effective enough to do so. I have since already started using a different iphone, and harvested the old monitor for it, but I’d like to get it up and running if at all possible.

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